Solving Quadratic Equations: (-2,5), (2.5,18.5) Answers Explained

In summary, the conversation discusses solving equations for a straight line and a curve, specifically 3x+11=2xsquared+2x+5 at the intersection. The equation is factorized to (2x+4)(x-2.5) and the solutions for x and y are found to be (-2,5) and (2.5,18.5). The textbook's answers are given as (-1.5,6.5) and (2,17), resulting in confusion and a realization of miscalculation. The conversation ends with gratitude for the help provided.
  • #1
bob4000
40
0
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 equation:

(2x+4)(x-2.5)

when i multiplied it out to check it i got: 2xsquared-x-6=0, which is alrite

when going on to solve x and y, i end up with:

x=-2
x=2.5
putting these into y=3x+11 i got:

y=5
y=18.5

finally giving the intersections of (-2,5) and (2.5,18.5)

however the answers given by the textbook from which the question was taken from, the intersections are (-1.5,6.5) and (2,17)

im really confused and would be much obliged for any help given

thank you
 
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  • #2
Is 4*2.5=6?
 
  • #3
its 4*-2.5=-6
 
  • #4
Remarkable. My calculator says that 4* -2.5= -10.

4*(2- .5)= 6
 
  • #5
4*(-2.5)=-10
 
  • #6
omg! i feel so goddamn stupid! :blushing:

thnx guys. i don't think i should be doing as level maths if i can't do 4*-2.5!

thnx again.
 

Related to Solving Quadratic Equations: (-2,5), (2.5,18.5) Answers Explained

What is a quadratic equation?

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It can have one or two solutions, depending on the value of the discriminant b^2 - 4ac.

What are the steps to solving a quadratic equation?

The steps to solving a quadratic equation are:

  1. Write the equation in standard form: ax^2 + bx + c = 0.
  2. Identify the values of a, b, and c.
  3. Calculate the discriminant: b^2 - 4ac.
  4. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions.
  5. Use the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, to solve for x.
  6. Check your solutions by plugging them back into the original equation.

What do the points (-2,5) and (2.5,18.5) represent in the context of solving quadratic equations?

In the context of solving quadratic equations, these points represent the solutions to the equation. Each point is in the form (x, y), where x is the value of the variable and y is the corresponding value of the equation when x is substituted in. For example, (-2,5) represents the solution x = -2, and when x = -2 is substituted into the equation, the resulting value is y = 5.

How do I know if my solution to a quadratic equation is correct?

To know if your solution to a quadratic equation is correct, you can plug the solution back into the original equation and see if it satisfies the equation. If it does, then it is a valid solution. Additionally, you can graph the equation and see if the point representing the solution falls on the graph.

Can a quadratic equation have more than two solutions?

No, a quadratic equation can have at most two solutions. This is because a quadratic equation is a second-degree polynomial and has a maximum of two roots. However, a quadratic equation can have fewer than two solutions or no real solutions, depending on the value of the discriminant.

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