Question

1 find the discriminant of each quadratic equation then state the number and type of solutions. -5x² - x + 4 = 0 the discriminant is \boxed{}, and there is/are two real solution(s).

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=-5$, $b=-1$, $c=4$.

Step2: Apply discriminant formula

Discriminant $D = b^2-4ac$
$D = (-1)^2 - 4(-5)(4)$

Step3: Calculate the discriminant

$D = 1 + 80 = 81$

Step4: Analyze solution type

Since $D>0$, there are two distinct real solutions.

Answer:

The discriminant is $81$, and there is/are two real solution(s).