Question

Given the solutions to a quadratic equation are x = − 3 and x = 6 , write the equation, in standard form, that generates these answers.

Answer 1

Answer: x^2 - 3x - 18 = 0

Explanation:

Since the solutions are x = -3 and x = 6, another way this could be written is (x+3)(x-6) = 0 (*This is because either x+3 or x-6 must equal 0 to make this true. So when you set x+3 = 0 or x-6= 0, you get the solutions x = -3 and 6)

After this, you can FOIL* the equation above, (This is a method where the first, outside, inside and last terms of the binomials are multiplied together to get the solution.)

So we get: x*x + x*-6+ x*3 + 3*-6 = 0

We can then simplify to get x^2 - 3x - 18 = 0.

*I hope I explained this well enough, but for more information try googling Zero property with binomials for the first part and FOIL method for the second part. Hope this helps :)