Question

11.Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

Answer 1

Given:

We will write the equation for the quadratic equation that will have solutions of x = 12 and x = 2

So, the factors of the equation will be:

(x - 12), and (x-2)

So, the factored form of the equation will be:

`(x-12)(x-2)=0`

Expand the equation to write it in standard form:

`\begin{gathered} (x-12)(x-2)=0 \\ x(x-2)-12(x-2)=0 \\ x^2-2x-12x+24=0 \\ x^2-14x+24=0 \end{gathered}`

So, the answer will be, the quadratic equation is:

`x^(2)-14x+24=0`