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}=(-7\pm17)/(4)`

So we have two solutions:

`\begin{gathered} x_1=(-7+17)/(4)=(10)/(4)=2.5 \\ x_2=(-7-17)/(4)=-(24)/(4)=-6 \end{gathered}`

Then the answers are -6 and 2.5.