Question

Please help if you know anything about polynomials, thank you

Answer 1

Given

$f(x)=\frac{x^2-5x-14}{q(x)}$

We want to find a possible graph of f(x)

Solution

First, notice the numerator of the function f(x)

It can be factorised

$\begin{gathered} f(x)=\frac{x^2-5x-14}{q(x)} \\ f(x)=\frac{(x-7)(^{}x+2)}{q(x)} \end{gathered}$

This mean that x = 7 and x = -2 are the roots of f(x)

This implies that the graph of f(x) must cross the x-axis at x = 7 and x = -2

By going through the option the correct option is B

Thus, from the graph above, It shows that only option B graph pass through x = 7 and x = -2

The right option is B