Question

If the solutions of plx)= 0 are=14 and 11, which function could be p?

Answer 1

We know that a parabolla is given by the form:

$p(x)=ax^2+bx+c$

We also know that we can factor this equation to get the form:

$p(x)=(x-h)(x-k)$

Where

$p(h)=0\text{ and }p(k)=0$

This is, h and k are the roots.

Then we can write:

h = 14

k = 11

$p(x)=(x-14)(x-11)$

We can also doing the multiplication to give the answer is standard form a parabolla:

$\begin{gathered} p(x)=(x-14)(x-11)=x^2-11x-14x+154 \\ p(x)=x^2-25x+154 \end{gathered}$

And that's a function as aked in the problem.