Question

find the discriminant of each quadratic equation then state the number and type of solutions.
$-4m^2 - 5m - 8 = 0$
the discriminant is \boxed{ }, and there is/are \boxed{ } \boxed{ } solution(s).

Explanation:

Step1: Identify quadratic coefficients

For $-4m^2 -5m -8=0$, $a=-4$, $b=-5$, $c=-8$

Step2: Apply discriminant formula

Discriminant: $\Delta = b^2 - 4ac$
$\Delta = (-5)^2 - 4(-4)(-8)$

Step3: Calculate discriminant value

$\Delta = 25 - 128 = -103$

Step4: Analyze solution type

Negative discriminant means 2 complex (non-real) solutions.

Answer:

The discriminant is $\boldsymbol{-103}$, and there is/are $\boldsymbol{2}$ $\boldsymbol{\text{non-real (complex)}}$ solution(s).