Question

evaluate the discriminant and determine the number and type of solutions to the equation.
$4x^2 - 5x + 4 = 0$
progress: 0/2
part 1 of 2
discriminant: \boxed{}

Explanation:

Step1: Identify quadratic coefficients

For $4x^2 -5x +4=0$, $a=4$, $b=-5$, $c=4$

Step2: Apply discriminant formula

Discriminant: $\Delta = b^2 - 4ac$
$\Delta = (-5)^2 - 4(4)(4)$

Step3: Calculate discriminant value

$\Delta = 25 - 64 = -39$

Step4: Classify solutions

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

Answer:

Discriminant: $-39$
Number and type of solutions: 2 distinct complex (non-real) solutions