Chapter 3.1, Problem 49E

To determine

To calculate: The zeros of the given function.

Answer to Problem 49E

The required solutions are $x=-10,3$ .

Explanation of Solution

Given information:

The function: $h\left(x\right)=x^2+7x-30$

Calculation:

The given function is $h\left(x\right)=x^2+7x-30$ .

To find the zeros of the given function, substitute 0 for $h\left(x\right)$ .

  $x^2+7x-30=0$

To solve the given equation by factoring, split the middle term with respect to the product of the coefficient of $x^2$ and the constant term.

  $\begin{array}{c}{x}^2+7x-30=0\\ x^2+10x-3x-30=0\end{array}$

Take the common factor x from the first two terms and $-3$ from the last two terms.

  $\begin{array}{c}{x}^2+10x-3x-30=0\\ x\left(x+10\right)-3\left(x+10\right)=0\\ \left(x+10\right)\left(x-3\right)=0\end{array}$

Solve the above expression for x .

  $\begin{array}{c}x+10=0\\ x=-10\end{array}$

And, $\begin{array}{c}x-3=0\\ x=3\end{array}$

Hence, the required solutions are $x=-10,3$ .