Chapter 12.4, Problem 15WE

To determine

To write: the value of the discriminant of given equation and to find the number of different real numbers roots in the equation.

Answer to Problem 15WE

The value of the discriminant is 0.

The number of different real roots is one.

Explanation of Solution

Given information:

Given equation,

  $y=x^2+16-8x$

Calculation:

Consider the given equation:

  $y=-x^2+3x+6$

The discriminant the equation is given by:

  $D=b^2-4ac$ , where $a=-1,b=-8$ and $c=16$

Now, evaluate the discriminant as shown:

  $\begin{array}{c}D=b^2-4ac\\ ={\left(-8\right)}^2-4\left(1\right)\left(16\right)\\ =64-64\\ =0\end{array}$

So, the value of the discriminant is 0.

Since D is zero.

  $\therefore$ The number of different real roots is one.

Since the coefficient of $x^2$ is positive, the parabola opens upward.