Question

evaluate the discriminant and determine the number and type of solutions to the equation. $4x^2 - 6x + 8 = 0$ progress: 0/2 part 1 of 2 discriminant: \boxed{}

Explanation:

Step1: Identify quadratic coefficients

For $4x^2 - 6x + 8 = 0$, $a=4$, $b=-6$, $c=8$

Step2: Apply discriminant formula

Discriminant: $\Delta = b^2 - 4ac$
$\Delta = (-6)^2 - 4(4)(8)$

Step3: Calculate the discriminant

$\Delta = 36 - 128 = -92$

Step4: Analyze discriminant sign

Since $\Delta < 0$, there are 2 distinct non-real (complex) solutions.

Answer:

Discriminant: $-92$
Number and type of solutions: 2 distinct complex (non-real) solutions