Question

Scott was given the function f(x) = x² + x – 12, andbelieves that the roots are —3 and 4. Is he correct?Explain or show your reasoning.

Answer 1

You have the following function:

f(x) = x² + x - 12

In order to find the roots of the previous function, use the quadratic formula:

$f(x)=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}$

take into account that the general for of a quadratic function is:

f(x) = ax² + bx + c

by comparing the previous function with the given function of the question you have:

a = 1, b = 1, c = -12

repalce these values into the quadratic formula:

$\begin{gathered} x=\frac{-1\pm\sqrt[]{1^{2}-4(1)(-12)}}{2(1)} \\ x\text{ =}\frac{-1\pm\sqrt[]{49}}{2} \\ x=\frac{-1\pm7}{2} \end{gathered}$

from the previous expressio for x, you obtain two solutions:

x = (-1-7)/2 = -8/2 = -4

x = (-1+7)/2 = 6/2 = 3

Hence, the roots of the given function are -4 and 3. And Scott is wrong