Question

evaluate the discriminant for the following equation. then complex numbers.
$2x^2 + 7x + 5 = 0$
the discriminant is \boxed{}. (simplify your answer.)

Explanation:

Step1: Recall discriminant formula

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

Step2: Identify coefficients

In the equation \(2x^2 + 7x + 5 = 0\), we have \(a = 2\), \(b = 7\), and \(c = 5\).

Step3: Substitute into formula

Substitute \(a = 2\), \(b = 7\), and \(c = 5\) into the discriminant formula:
\(D = 7^2 - 4\times2\times5\)
\(= 49 - 40\)
\(= 9\)

Answer:

\(9\)