Question

use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, \\(4x^{2}+19x + 25 = 0\\) which of the following correctly describes the solutions to the given equation? \\(\bigcirc\\) a. a repeated real solution \\(\bigcirc\\) b. two unequal real solutions \\(\bigcirc\\) c. no real solution

Explanation:

Step1: Identify quadratic coefficients

For $4x^2 + 19x + 25 = 0$, $a=4$, $b=19$, $c=25$

Step2: Calculate discriminant

Discriminant formula: $\Delta = b^2 - 4ac$
$\Delta = 19^2 - 4(4)(25)$
$\Delta = 361 - 400 = -39$

Step3: Analyze discriminant sign

Since $\Delta < 0$, no real roots exist.

Answer:

C. No real solution