Question

use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation.
$4x^2 - 21x + 25 = 0$

which of the following correctly describes the solutions to the given equation?
a. two unequal real solutions
b. no real solution
c. a repeated real solution

Explanation:

Step1: Identify quadratic coefficients

For $4x^2 -21x +25=0$, $a=4$, $b=-21$, $c=25$

Step2: Calculate discriminant

Discriminant formula: $\Delta = b^2 -4ac$
$\Delta = (-21)^2 -4\times4\times25$

Step3: Compute discriminant value

$\Delta = 441 - 400 = 41$

Step4: Analyze discriminant sign

Since $\Delta=41>0$, there are two unequal real solutions.

Answer:

A. Two unequal real solutions