Quadratic equations Definition and 97 Threads

Homework Statement The equation kx2 - 3x + (k+2) = 0 has two distinct real roots. Find the set of possible values of k. Homework Equations Since the equation has two distinct real roots, b2 - 4ac > 0 The Attempt at a Solution b2-4ac>0 9-4(k+2)(k)>0 9-4(k2+2k) >0 9-4k2-8k>0 =...

Homework Statement Is it true that all quadratic equations (ax2+bx+c) can be factorised into this form: (ax+b)(cx+d)? I think so, but I'm not certain.

Is the discriminant, of the quadratic equations, the difference between the two roots? Or is it a special case?

Homework Statement What will be the values of 'm' so that the range of the equation y= \frac{mx^2+3x-4}{-4x^2+3x+m} will be all real values i.e. y\epsilon (-\infty,\infty)given:x can take all real values. any help or hint will be appreciated. Homework Equations The Attempt at a Solution i...

Homework Statement There are 2 beakers P and Q. P contains 50 litres of water and Q contains 40 litres of acid. x litres is taken from both the beakers, mixed and replaced. This process is repeated 2 times and after the second time, there is 71/8 litres of acid in P. What is the quantity of...

Hey, I have a set of quadratic equations in the form of: ax^2 -bxy + cy^2 = d ax^2 -bxz + cz^2 = d ay^2 -byz + cz^2 = d where a,b,c,d are given constants. I am really stuck trying to figure out the values of x,y,z :confused: My previous trial, was attempting to solve it as a...

1. An Acapulco diver dives into the sea from a height of 35 m. His height h metres t seconds after leaving the cliff is given by h=-4.9t^2+t+35. How long is it until he reaches the water? How long does it take him to fall from 35 m to 25 m? 2. (-b +/-(sqrt)b^2-4ac)/2b 3. I don't have any work...

This is something that's been bothering me for a while... If quadratics are any polynomials that have a degree of 2, then would that make the following equations quadratics (I don't know what all of them are for by the way, they're just equations I'm pulling from my math book which doesn't...

Hi all, I am trying to generalize a geometric concept found on page 7 from Steven Weinberg's "Gravitation and Cosmology" from 2 to 3 dimensions. At the end I am stuck with the following set of equations: 1: a1+a2z32+a3z3z4+a4z42=0 2: b1+b2z32+b3z3z5+b4z52=0 3: c1+c2z32+c3z3z6+c4z62=0...

We have two unknown vectors x,y with real non negative values. We can assume ||x||=||y||=1. There are m known nxn matrices with real values. We have m equations of the form: yTA1x=0 ... yTAmx=0 What are the conditions for the existence of solutions for x,y? What is the minimal number m...

Need help solving some. I'll put up one for now. a/b-x + b/a-x = 2 I'm just looking for how to solve it, because I always reach 2x^2 - 3ax - 3bx + a^2 + b^2 + 2ab = 0 and get stuck. Please show me your steps. Thanks!

Homework Statement Given that the quadratic equation (m^2-3m-4)x^2+(m^2+2)x+12=0 has real roots a and b .Find the set of values of m such that a<-1<b Homework Equations The Attempt at a Solution By using the fact this equation has two real roots ,b^2-4ac>0.That's all i can see...

FUN solving Quadratic equations :) Homework Statement Marnie can walk 1km/h faster than Jon. She completes a 20 km hike 1 hour before him. Write an equation ans solve it and find their walking speeds. Homework Equations speed= distance/time the quadratic equation The Attempt at a...

Homework Statement Find the time required for a train to reach 100m if V0=20m/s and acceleration is 0.5m/s2 Homework Equations s=v0t+(1/2)at2 The Attempt at a Solution i am not sure of how to go about getting s=(20)t+(1/2)0.5t2 into quadratic form for use in the quadratic formula...

Hey there! I just want to know that this problem (t-2)^2=36 can be solved by squaring t-2 so we have the answer as t=8 ,-4 but suppose if I rather do like this that I square root 36 and remove the power on t-2 then or t- 2= 6 or t=8 here also i get the 8 result but i don't...

Homework Statement For the quad equation x^2 - px + 9 = 0 1. Write down the sum of roots and product of roots 2. Find p IF twice the sum of the roots EQUALS the product 3. Find p IF the roots are unequal Homework Equations Sum = (a+b) = -b/a Product = (ab) c/a The...

While a problem, this is more for me to learn to help my kid with her own homework. I used to be great at this sort of thing but for some reason I just can't get my head around this one. -125 = 39.1t - 4.9t^2 I need to find the value for t. It should be approx 10.4. I would just like to...

I know this is probably really easy, but i just can't figure it out.. Homework Statement Find values of k for which (5 + 4x - x^2 = k) has equal roots. I know the answer is k = 9 but i don't know how to get there.. Homework Equations ax^2 + bx + c = 0 Discriminant = b^2 - 4ac...

Homework Statement Find the roots and the vertex for 3x^2 + 5x - 2 Homework Equations ax^2 + bx + c a(x - h) + k The Attempt at a Solution OK, this is what I attempted. 3x^2 + 5x - 2 = 0 3x^2 + 6x - x - 2 = 0 3x(x+2) - 1(x+2) = 0 x = 1/3 and x = -2 OK, so I found the roots...

First of all, I searched the forums and couldn't really find one on how to approach a quadratic equation that has brackets. Here is the equation: y=(x+1)2 - 2 My teacher told me to factorize by sight in pairs and i used this equation for it: ax2+bx+c. I think c=-2 but I don't know how to get...

Homework Statement If x is real and p = \frac{3(x^{2}+1)}{2x-1}, prove that p2 - 3(p+3) \geq 0. Homework Equations ax2 + bx + c = 0 x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} Nature of the Roots of a Quadratic Equation: If b2 - 4ac is positive, quadratic equation has two real &...

how do you calculate the equation of a quadratic curve. A straight line curve uses y-y1=m(x-x1) is i an alteration of this line? cheers

Homework Statement I just need some guidance regarding how to work out the value of x in the quadratic equation. I don't want you guys to do the work for me, I just want to know how to figure it out. Thanks Homework Equations The Attempt at a Solution

Homework Statement Homework Equations \lim(\frac{(x^2)-2x-3}{(x^2)+5x+6}) x->(-2) The Attempt at a Solution anyone can help out on this one?

Homework Statement In the attached diagram, the displacement of a follower (y) changes as the angle of the cam changes (\vartheta). The follwer has a smooth velocity over the entire path. Therefore, the velocity must match on both sides of the four points noted on the graph. If we assume...

I got into college as a mature student and I'm doing well in all subjects except for math. I'm struggling a good bit because I never finished high school math and there's a lot of stuff they assume everyone knows but I don't. I have to study it at home so I can keep up. Its mainly quadratic...

Homework Statement Determine \int\frac{4x^{2}-2x+2}{4x^{2}-4x+3}dx Homework Equations I believe it's necessary to complete the square. The Attempt at a Solution Completing the square for 4x^{2}-4x+3 gives \int\frac{4x^{2}-2x+2}{(x-\frac{1}{2})^2+\frac{1}{2}}dx let...

I have a problem with determining eigenvalues. This is what I've got thus far: Homework Statement Identify and sketch the graph of the quadratic equation 4x² + 10xy + 4y² = 9The Attempt at a Solution We put it in the matrix form: \begin{pmatrix} 4 & 5 \\ 5 & 4 \\ \end{pmatrix} Now we find the...

Homework Statement Find the number of integral values of 'k' for which the quadratic equation 2x^2 +kx - 4=0 will have two rational solutions. Homework Equations d=(b^2- 4ac)^(1/2) The Attempt at a Solution If discriminant is a perfect square, then the roots will be rational and...

[SOLVED] Quadratic Equations How would I find what 'a' and 'q' is in the equation of y=a(x)^2+q when I'm given 2 plots? Example:Find 'a' and 'q' so that a parabola y=ax^2+q passes through each pair. a)(-3,11)and(4,18) if you could give me step by step explanation that would be much...

In college we have been given an exercise about Quadratic Equations, before the actual assignment. We have been told that we need to use three different methods for three different equations. The methods are: The Quadratic Formula, Factorization and Graphical. We have been given three...

i learned this a few weeks ago and now i have a project due tomorrow and i want to make sure in doing this right before i make useless graphs... like: (x-1)^2+3 or (x+2)^2 i can't remember how to exponent that ****...

[SOLVED] Quadratic Equations and Inequalities question about properties of quadratic so here is the question graph the function. state the domain and range of the function. F(x)=-2x^2-3x+2 i try and use the axis of symmetry (-b/2a) and then plug that into the original formula to get the...

All, I am not sure how to handle this situation with complex numbers. Can you help? Q = A^2 + ABi Where Q is a complex number. Can we not solve for A if we know Q and Bi using a quadratic equation? 0 = A^2 + ABi + -Q Let... Q = 455 Bi = -22 And in this case I do know...

I am stuck on this problem. I can reach the correct answer with the quadratic formula, but not with the method suggested (completing the square). Thanks in advance. The problem is: 2x^2+8x+1=0 This is what I tried: 2x^2+8x=-1 2(x^2+4x)=-1 2(x^2+4x+4)=-1+8 2(x+2)^2=7...

Today, I tried to translate the very basic "solve quadratic equations" program I made a while back in Python to C++. [SIZE="1"] #Solving quadratic equations import math print print "Please enter information in accordance with ax^2 + bx + c = 0" a =...

How do you solve quadratic equations which have atleast one positive root?? The question was this: Find the value of 'm' for which the roots are such that at least one is positive. x2 -(m-3)x + m = 0 mR. Can someone help me get started? Here is my work: I checked the discriminant. for...

hi, I need to learn very well about quadratic equations. Can anyone give me a site to learn about these equations? Thanks:smile:

hey can you help me solve these, I've got 20 problems..and i only need is this problem so that i have an idea of answering the others An engineer can decrease by 2 hours the time it takes to travel 200km. If he increases the speed of the freight train by 5km per hour, what is the original...

hey , i tried deriving another method for solving a quadratic equation ,and here is wat i came across +or - sqrt ([b^2-2ac+or-(b sqrt[b^2-4ac])/2a^2) i hope u get this correctly its read plus or minus square root of b^2-2ac plus or minus b root b^2-4ac all divided by 2a^2,remember the...

Hi, How is the roots of a quadratic equation related to the distance from the x-axis at where the root is - where ... ax^2+bx+c=0 and ... x = (-b +- SQRT(b^2-4ac))/2 Can someone help me to establish where this distance relationship to the x-axis and the root come from? Thx! LMA

The quadratic equation x^2 + mx + n = 0 has roots that are twice those of x^2 + px + m = 0, and none of m, n, p is zero. What is the value of n/p? I'm stuck and don't know where to begin.

Hey I have a test today and can't figure out how to solve certain quadratic equations. We are doing solving the equations by completing the square using these steps: 1. divide each side by coefficient of x squared 2. rewrite the equation with the constant on right side 3. complete the...

y=4x^2-8x-5 Find the coordinates of the turning point of the curve. Where do I even start?

I just need to know the basics of 2 ways to excecute a quadratic equation...: Quadratic formula and factoring. Thankyou!

hey there reader i have: y=3x+11 y=2xsquared+2x+5 i have to solve these as they are represent a straight line and a curve respectively. so far i have: 3x+11=2xsquared+2x+5 at the intersection ;2xsquared-x-6=0 i factorised this and checked it to make sure it matched the above...

Any idea how to figure this problem out? x + 1 = 9x^3 + 9x^2