Question

A certain quadratic polynomial has solutions x=4 and x=0. Create an equation that could represent this quadratic polynomial.

Answer 1

(x-4)x = 0

Explanation:

If we have a quadratic equation of the form

`(x-a)(x-b)=0`

it has solutions at x = a and x = b because putting either one of these values into the above equation satisfies it. For example, putting in x = a gives

`\begin{gathered} (a-a)(x-b)=0 \\ 0(x-b)=0 \\ 0=0 \end{gathered}`

this satisfies the equation and likewise for x = b.

Hence, if we want to construct an equation which has solutions x = 4 and x = 0, we just need to set a = 4 and b = 0. Doing this gives

`\begin{gathered} (x-4)(x-0)=0 \\ (x-4)x=0 \end{gathered}`

which is a polynomial that has the solutions desired.