Question

Use the given function f to find f(0) and solve f(x) = 0. Show work

f(x) = x^2 - x - 12

Answer 1

1) Substitute 0 for x in the function:

$$f(0)={{0}^{2}}-0-12=-12$$

so

$$f\left( 0 \right)=-12$$

2) Solve

$$f\left( x \right)=0$$

We have equation

$${{x}^{2}}-x-12=0$$

In order to solve this equation we use the quadratic formula. If 

$$a{{x}^{2}}+bx+c=0$$

then

$$x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$$

In our case

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

Substitute these numbers in the formula

$$x=\frac{-\left( -1 \right)\pm \sqrt{{{\left( -1 \right)}^{2}}-4\cdot 1\cdot \left( -12 \right)}}{2\cdot 1}$$

$$x=\frac{1\pm \sqrt{1+48}}{2}$$

$$x=\frac{1\pm \sqrt{49}}{2}=\frac{1\pm 7}{2}$$

$${{x}_{1}}=\frac{1+7}{2}=4,\,\,\,\,{{x}_{2}}=\frac{1-7}{2}=-3$$

So our solution is

$${{x}_{1}}=4,\,\,{{x}_{2}}=-3$$