Chapter 11.6, Problem 4BCYP

To determine

To calculate: The simplified form of the given expression.

Answer to Problem 4BCYP

The required values of the variable x is $4,-2,7,-2$ .

Explanation of Solution

Given information:

The given expressions are:

  $x^2-2x-8$ and $x^2-5x-14$

Formula used:

Quadratic formula:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Consider the given expression

  $x^2-2x-8=1x^2+(-2)x+(-8)$

Use the quadratic formula to simplify the expression

Substitute $-2$ for b , $1$ for a and $-8$ for c .

  $\begin{array}{c}x=\frac{-\left(-2\right)\pm \sqrt{{\left(-2\right)}^2-4\times 1\times \left(-8\right)}}{2\times 1}\\ =4,-2\end{array}$

Consider the given expression

  $x^2-5x-14=1x^2+(-5)x+(-14)$

Use the quadratic formula to simplify the expression

Substitute $-5$ for b , $1$ for a and $-14$ for c .

  $\begin{array}{c}x=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\times 1\times \left(-14\right)}}{2\times 1}\\ =7,-2\end{array}$

Hence, the required values of the variable x is $4,-2,7,-2$ .