Answer
The discriminant is $0$.
There is one real solution to the equation.
Work Step by Step
First, rewrite the equation in quadratic form, which is given as $ax^2 + bx + c = 0$:
$2x^2 - 8x + 8=0$
In a quadratic equation, the discriminant is found within the Quadratic Formula.
The Quadratic Formula is given as:
$x = \frac{-b ± \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the squared term, $b$ is the coefficient of the linear term, and $c$ is the constant term.
The expression $b^2 - 4ac$ within the radical is called the discriminant. The discriminant can determine how many solutions there are and whether the roots are real or imaginary.
In this exercise, $a = 2$, $b = -8$, and $c = 8$. Plug these values into the discriminant:
$(-8)^2 - 4(2)(8)$
Evaluate the exponent first:
$64 - 4(2)(8)$
Do the multiplication:
$64 - 64$
Subtract:
$0$
If the discriminant is positive, the equation has two real solutions.
If the discriminant is zero, there is one real solution.
If the discriminant is negative, then there are two imaginary solutions.
In this exercise, the discriminant is zero; therefore, there is one real solution to the equation.
