Chapter 9.4, Problem 60HP

To determine

Find the value of c.

Answer to Problem 60HP

  $c=64$

Explanation of Solution

Given Information: $4x^2-32x+c=0$

Calculation:

  $4x^2-32x+c=0$

If the discriminant of a quadratic function is equal to zero, that function has exactly one real root and crosses the x-axis at a single point. For this, $b^2-4ac=0$

As the general equation $y=a{x}^2+bx+c$ (1)

Now,

  $a=4,b=-32$

So, simplify

  $b^2-4ac=0$

Now,

  ${\left(-32\right)}^2-4\times 4\times c=0$

Now,

  $1024-16c=0$

Now,

  $c=\frac{1024}{16}$

Hence,

  $c=64$