Question

compute the value of the discriminant and give the number of real solutions of the quadratic equation
$-5x^2 - x - 2 = 0$

discriminant:

number of real solutions:

Explanation:

Step1: Recall discriminant formula

For quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).
Given equation \(-5x^2 - x - 2 = 0\), so \(a = -5\), \(b = -1\), \(c = -2\).

Step2: Calculate discriminant

Substitute values into formula:
\(D = (-1)^2 - 4\times(-5)\times(-2)\)
\(= 1 - 40\)
\(= -39\)

Step3: Determine real solutions

If \(D < 0\), no real solutions; \(D = 0\), one real solution; \(D > 0\), two real solutions.
Since \(D = -39 < 0\), number of real solutions is 0.

Answer:

Discriminant: \(-39\)
Number of real solutions: \(0\)