Quadratic equation Definition and 252 Threads

Homework Statement Get an inverted quadratic equation (-x^2) with maximum y=100 and roots x=0 and x=1/120. Homework Equations The Attempt at a Solution I tried changing the several terms of the quadratic equation, used the quadratic formula setting c=100, and x=0 with the...

Homework Statement How should be the value of a so quadratic equation ax^2-4x+4=0 to have double solutions? A)\;\;2 B)\;\;1 C)\;-1 D)\;-2 Homework Equations The Attempt at a Solution D=b^2-4ac If: D>0\;\;\rightarrow\; {x_1,x_2}\;\rightarrow\;\text{double solutions.}...

Homework Statement Two platforms 50m in height have targets on them. An object succeeds in impacting with both of these. S=ut + ½ at2 can be rearranged into the form: ½ at2 + ut – s =0 This is a quadratic equation. [ ax2 + bx +c =0 ] Use this to calculate: I. The times at which the...

Homework Statement \alpha and \alpha^{2} are two roots of the equation x^{2} -12x + k = 0 Find 2 values for k. The Attempt at a Solution \alpha + \alpha^{2} = 12 \alpha^{3} = k I have no idea where to go from here. Any help appreciated.

Homework Statement Solve using the formula method. Homework Equations 3t^2+7t=5 The Attempt at a Solution 3t^2+7t-5=0 t= \frac{-7 +or-\sqrt{7^2-4(3)(-5)}}{2(3)} t= \frac{-7+\sqrt{109}}{4} t= -4.39 OR... t= \frac{-7-\sqrt{109}}{4} t= -9.61 The reason I have doubts is...

Homework Statement Find the intervals of all possible value of p which the equation equation: (p-1)x^2+4x+(p-4)=0 has two different roots. Homework Equations ax^2+bx+c>0 ?? The Attempt at a Solution (p-1)x^2+4x+(p-4)>0 ?? How would I go about solving this? Is two roots...

Can anyone tell me how to calculate the discriminant of a general equation of 2 degree in 2 variables, ax^{2}+by^{2}+2gx+2fy+2hxy+c=0? Thanks!

Homework Statement given that kλ2-ρcpuλ-ρcpωi=0 plug into the quadratic formula and get out an equation that looks like this λ=α+iβ±γ√(1+iδ) where α,β,γ,and δ are in terms of ρ,cp,u,k, and ω Homework Equations (-b±√b2-4ac)/2a kλ2-ρcpuλ-ρcpωi=0 λ=α+iβ±γ√(1+iδ) The Attempt at a...

√(2gH)(M-m)=mV+M√((2gH(M+m)-mV^2)/M) Solve for V in terms of given terms.

Maths Quadratic Question Homework Statement Find the interval in which 'm' lies so that the expression \frac{mx^2+3x-4}{-4x^2+3x+m} can take all real values ,where x is real. The Attempt at a Solution i have equated this equation to y y=\frac{mx^2+3x-4}{-4x^2+3x+m}...

Homework Statement Find the least integral value of k for which the quadratic polynomial (k-2)x2 + 8x + k+4 > 0 where x is real. The Attempt at a Solution i am trying to solve the discriminant by equating it to>0 D>0 but i don't think it is correct. Please...

Homework Statement if ax2+2bx+c=0 and a1x2+2b1x+c1 have a common root and a/a1 ,b/b1 ,c/c1 are in A.P. show that a1,b1,c1 are in G.P. Homework Equations The Attempt at a Solution I know the mean formula of A.P. i.e. the middle term is the mean of the other two. any hints...

Homework Statement If 3x2+2αxy+2y2+2ax-4y+1 can be resolved into two linear factors, prove that α is the root of the equation x2+ 4ax+2a2+6=0. please don't solve the problem just hint is expected.

Homework Statement f(x)=6x^2+9x-6 Where does this function intersect the x-axis (i.e. what are the roots or zeroes of f(x))? Solve by factoring using the Box Method. When I use the method that is shown on this website http://www.purplemath.com/modules/factquad2.htm for this...

Homework Statement Find the zeros of the quadratic equation? Homework Equations P(x)=4(x+7)^2+(x+7)-3 The Attempt at a Solution I substituted and made it 4u^2+u-3 ?? Then after that I factor then back substitute?? I'm not sure how to back substitute tho.

Hi there! I'm working on analyzing some data from an experiment, and you can see a graph of some of the results in the attached .jpg image. I've done both a linear and a quadratic fit on the data points, weighted to error bars (the red lines are the fits). I use percents in the graph, but I'd...

"Find the rule of correspondence for a quadratic equation that is the same shape as y=x^2, with the only given information being x-intercepts at (-3, 0) and (1, 0)." I cannot for the life of me figure this out, and it's making me feel extremely stupid. I know the answer to the question is y=...

Given an equation in the form 0 = ax2 + bx + c, why is it not possible to simply differentiate both sides, and produce 0 = 2ax + b, and solve for x, instead of going through the drudgery of the quadratic equation? My knowledge of calculus tells me that it is because 0 = ax2 + bx + c is not a...

Homework Statement A (complex) solution to the quadratic equation of the form z^2 + α z + β = 0, is z = 1 + i. (where α and β are real numerical constants), Write down the other solution and hence determine the values of α and β. Homework Equations The Attempt at a Solution this question...

Homework Statement if roots of the equation ax^2+bx+c=0 be the form of p/(p+1) and (p-1)/p,the the value of (a+b+c)^2 is? Homework Equations The Attempt at a Solution

Homework Statement I just would like to know how would I isolate x in a quadratic equation such as y = x(3-x). Homework Equations quadratic equation. The Attempt at a Solution I don't think you can use completing square in this, and quadratic equation doesn't really...

http://www.cs.odu.edu/~toida/nerzic/content/problem_solving/problem_solving.html example 3 ========================================= Quote Problem: Given that a, b, and c are odd integers, prove that equation ax2 + bx + c = 0 can not have a rational root. Understanding the Problem: This is a...

Homework Statement Solve 2kx^2 - (k+1)x + 4 by completing the square Homework Equations 2kx^2 - (k+1)x + 4 The Attempt at a Solution What I have so far: -> x^2 - (k+1/2k)x + 4/2k = 0 -> x^2 - (k+1/2k)x + ((k+1/2k)/2)^2 - ((k+1/2k/2)^2 + 2k = 0 -> x^2 - (k+1/2k)x +...

Homework Statement Find the exact (surd) answer Homework Equations -2kx^2 + 4x +6k = 0 The Attempt at a Solution Attempt 1 (quadratic formula method) -2kx^2 + 4x +6k = 0 -> -(-2) +- sqrt((-2)^2 - (4 x k x -3k)0 / 2k -> 2 +- sqrt(4+12k^2) / 2k -> 2 +- sqrt(4(1+3k^2)...

Homework Statement Solve the quadratic equation z^2 + 4(1 + i(3^0.5))z - 16 = 0 Homework Equations The Attempt at a Solution I think I've done this correctly, I just wanted to verify. I've only done the solution for k=0...

Homework Statement Solve the equation 2cos^2\theta + 5cos\theta - 3 = 0\ for\ \frac{3\pi}{2}<\theta<5\pi Homework Equations quadratic equation, power reduction formula: cos^2\theta = \frac {1+cos2\theta}{2} The Attempt at a Solution First I tried using the quadratic...

Homework Statement Consider the general quadratic function f(x)=ax2+bx+c with a>0. By calculating the minimum value of this function, show that f(x)\geq0 for all x if and only if b2-4ac\leq0 Homework Equations The Attempt at a Solution I know that the min for a quadratic equation...

Homework Statement If one of the roots of the quadratic equation, ax^2+bx+c=0 is m+ni, show that the other root is m-ni. Homework Equations The Attempt at a Solution How do i actually show this? I mean it's a well known fact and a direct outcome of the quadratic formula. Is this...

Homework Statement Given that for all values of x: 3x^2 + 12x + 5 = p(x +q)^2 + r a) find the values of p, q and r b) solve the equation 3x^2 + 12x + 5 = 0 The Attempt at a Solution I'm completely lost here but here's my attempt at a solution - I'm pretty sure that I did it...

Homework Statement The solution of the quadratic equation x2 - 11x + 22 = 0 are x = 3 or x = 6. What is the base of the numbers? Homework Equations Knowledge of how to convert from a generic base to decimal? The Attempt at a Solution I tried to just place r in where I would...

Homework Statement 2n=n2 Homework Equations The Attempt at a Solution I know the solution is 2 and 4. But I have no idea how to solve it without guessing...

Homework Statement How do I simplify the transformation of this equation? y=-2[-1/3(x+2)]^2-4 Homework Equations af(k(x-d))+c The Attempt at a Solution If this was a linear equation I would simply distribute the -1/3 into (x+2) and then distribute -2 into the (-1/3x -2/3)...

Homework Statement 4n^2+9m^2-240n-720m+18000=0 Find n+m Homework Equations The Attempt at a Solution I try to express the equation in the form of a(n+m)^2-b(n+m)+c=0 but i couldn't find a way to do so .

express the following in terms of alpha1 x beta1 and alpha2 x beta2 alpha1 x alpha 2=beta1 x beta2

Okay so this seems like a very simple problem to me but I can't figure it out so I definitely need some help. I'm not a mathematician but a programmer and in this case I need to figure out how to get the curve that passes through 3 points. I know this can be done easily with substitution but...

Homework Statement The quadratric equation x^2 - 5x + 7 = 0 has the roots α and β. Find the quadratic equation with roots α^3 and β^3. Homework Equations N/a The Attempt at a Solution u = α^3 α = u^(1/3) u^(2/3) - 5(1/3) + 7 = 0 u^(1/3)[u - 5] = -7 --- minus 7 off each...

x2 + 3x + 2 = 0 (x + 1) (x + 2) so x = -1 or -2 Is that right?

Here is a quadratic equation along with its solution. There's only 1 thing I don't understand. In the brackets how do we know that the values are - 4 and - 5 as opposed to + 4 and + 5. Why are they both negative when the quadratic contains both a negative and a positive expression? x2 - 9 +...

The graph of y=(5-2x)^2+1. What are the transformations that have occurred from y=x^2. Im really confused with the transformations here.

Homework Statement These two questions are very similar: 1) Let c be a constant. If a and b are the roots of the equation x^2 + 2x - c = 0 then 2b-a^2 = ? 2) Let k be a constant. If a and b are the roots of the equation x^2 - 3x + k = 0 Then a^2 + 3b = ? Homework Equations...

Homework Statement How would you solve this problem: x^2 - 5x >= 0 Homework Equations The Attempt at a Solution I think it might be something to do with the Quadratic Formula?

Homework Statement Here the the word problem: Genelle and Eljen can paint a room together in 4 hours. Working alone, Genelle can paint the room in two hours less than Eljen can. Find how long it takes Eljen to paint the room alone. Homework Equations Maybe, this problem can be solved using...

Now what? Quadratic equation! Homework Statement A cannon having a muzzle speed of 1000 m/s is used to destroy a target on a mountaintop. The target is 2000m from the cannon horizontally and 800m above the ground. At what angle, relative to the ground, should the cannon be fired? Ignore air...

Homework Statement Solve the following equation for Z, find all solutions. z2 -2z + i = 0 Homework Equations [-b(+/-) sqrt(b2-4ac)]/2a The Attempt at a Solution Using the equation above, z = [2 (+/-) sqrt( (-2)2 - 4 (1) (i)) ]/ 2(1) =[2 (+/-) sqrt ( 4 - 4i)]/2 =...

Homework Statement Solve (a/2)x^2+vx-d=0 for x. Homework Equations Quadratic factoring, quadratic formula (?) The Attempt at a Solution I have no idea where to start with this question. It is probably the variables that are throwing me off, and as such I have no idea what I'm doing...

Hi! I have this Math 11 problem. I do my math through Distance Ed. and there are no examples like this one in the supplied lessons. If anyone could help me with this question, that would be great! Homework Statement Find the equation of the quadratic function with a vertex at (1,3) passing...

I understand how the discriminant, b^{2}-4ac, comes from in the quadratic equation ax^{2}+bx+c=0, but how does it come from the general quadratic equation ax^{2}+bxy+cy^{2}+dx+ey+f=0 ?

The general quadratic equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 How is this derived? How does the discriminant, B2 – 4AC determine the class of the conic section?

Homework Statement An object falls from height h from rest. If it travels .50h in the last 1.00 s, find (a) the time and (b) the height of its fall. Explain the physically unacceptable solution of the quadratic equation in t that you obtain. Homework Equations Pretty much any free...

Quadratic equation and absolute value... Consider equation |x2-2x-3|=m, m belongs to R If the given equation has no solution then find the interval in which the m lies. 2. Homework Equations -Given in question 3. Since this equation is in modulus there would be two equations...