Question

use the discriminant to determine the number and types of solutions of the quadratic equation.
$x^2 - 8 = 0$
the equation has

Explanation:

Step1: Identify quadratic coefficients

For $x^2 - 8 = 0$, we have $a=1$, $b=0$, $c=-8$.

Step2: Calculate discriminant

Discriminant formula: $\Delta = b^2 - 4ac$
$\Delta = 0^2 - 4(1)(-8) = 32$

Step3: Analyze discriminant value

Since $\Delta = 32 > 0$ and is not a perfect square, the equation has two distinct real irrational solutions.

Answer:

two distinct real irrational solutions