Question

Which of the following is a quadratic equation that has the roots x = 5 and x = 6?

Answer 1

the quadratic equation that has the roots x=5 and x=6 is;

`x^2-11x=-30`

Explanatio

We want to derive the quadratic equation that has the roots x=5 and x=6;

To derive the equation, we have;

`(x-5)(x-6)=0`

Expanding;

`\begin{gathered} x^2-5x-6x+30=0 \\ x^2-11x+30=0 \\ x^2-11x=-30 \end{gathered}`

Therefore, the quadratic equation that has the roots x=5 and x=6 is;

`x^2-11x=-30`