Question

Consider the function f(x)=2x2 + 7x-30What are the zeros of the function?

Answer 1

We have the following quadratic function:

$f(x)=2x^2+7x-30$

And we need to find its zeros i.e. the solutions to the equation:

$2x^2+7x-30=0$

Given a quadratic equation like the following:

$ax^2+bx+c=0$

Its solutions are given by the quadratic solving formula:

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

In our case we have a=2, b=7 and c=-30. Then we get:

$x=\frac{-7\pm\sqrt[]{7^2-4\cdot2\cdot(-30)}}{2\cdot2}=\frac{-7\pm\sqrt[]{49+240}}{4}=\frac{-7\pm\sqrt[]{289}}{4}$

So we continue:

$x=\frac{-7\pm\sqrt[]{289}}{4}=\frac{-7\pm17}{4}$

So we have two solutions:

$\begin{gathered} x_1=\frac{-7+17}{4}=\frac{10}{4}=2.5 \\ x_2=\frac{-7-17}{4}=-\frac{24}{4}=-6 \end{gathered}$

Then the answers are -6 and 2.5.