Question

compute the discriminant. then determine the number and type of solutions of the given equation.
$4x^2 - 5x + 7 = 0$
what is the discriminant?
\boxed{} (simplify your answer.)

Explanation:

Step1: Identify quadratic coefficients

For $4x^2 -5x +7=0$, $a=4$, $b=-5$, $c=7$

Step2: Apply discriminant formula

Discriminant: $\Delta = b^2 - 4ac$

Step3: Substitute values and calculate

$\Delta = (-5)^2 - 4(4)(7) = 25 - 112$

Answer:

$-87$

Additionally, since the discriminant $\Delta = -87 < 0$, the quadratic equation has 2 distinct complex (non-real) solutions.