Chapter 9, Problem 11PFA

To determine

To calculate value of c

Answer to Problem 11PFA

  $c=36$

Explanation of Solution

Given information :

The function provided is $x^2+bx+c$ .

The value of b that has been provided $b=12$

The trinomial is a perfect square.

Formula used :

To calculate the time when height of ball is 0 feet, use the formula to find roots of a quadratic equation. This can be found by using $t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Here ‘a’, ‘b’ and ‘c’ are the co-efficient of the given equation.

Here, $a=1\text{ and }b=12$ .

Calculation :

  $x=\frac{-12\pm \sqrt{{(12)}^2-4\times (1)\times (c)}}{2\times (1)}$

Putting the values in the formula.

  $x=\frac{-12\pm \sqrt{144-4c}}{2}$

For it to be a perfect square $144-4c$ should be equal to 0 .

  $144-4c=0$

Simplifying.

  $c=36$