Question

finding the discriminant of $4x^2 - 3x - 5 = 0$
a) $-89$
b) $-\sqrt{89}$
c) $89$
d) $\sqrt{89}$

Explanation:

Step1: Recall discriminant formula

For quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).

Step2: Identify coefficients

In \(4x^2 - 3x - 5 = 0\), \(a = 4\), \(b = -3\), \(c = -5\).

Step3: Substitute into formula

\(D = (-3)^2 - 4\times4\times(-5)\)
\(= 9 + 80\)
\(= 89\)

Answer:

89 (Option C)