Question

PLEASE HELP! Write the quadratic equation given the solutions x=-3 and x=4. How would I do this, step by step please?

Answer 1

If the roots are x = -4 and x = 3, then the equation would be:

(x+4) * (x-3) = 0

Multiply these factors together to get:

x^2 + x - 12 = 0

Since your c factor has to be 4, then you need to divide both sides of this equation by -3 to get:

-x^2/3 - x/3 + 4 = 0

This would be the same as:

-(1/3)*x^2 - (1/3)*x + 4 = 0

a would be equal to -(1/3)
b would be equal to -(1/3)
c would be equal to 4


If you were given this equation in this form to start with and asked to solve for the roots, you would have done the following:

Multiply both sides of the equation by (-3) to get:

x^2 + x - 12 = 0

Factor this equation to get:

(x-3) * (x+4) = 0

Solve for x to get:

x = 3
or:
x = -4

which is where you started from.

Answer 2

Thanks so much!

Answer 3

No problem! :)