Question

use the discriminant to answer the questions.
32x - 4 = 4x² + 60
for the equation shown, choose the description of
the solutions.
○ one real, rational
○ two real, rational
○ two real, irrational
○ two complex
done

Explanation:

Step1: Rearrange to standard quadratic form

$4x^2 - 32x + 64 = 0$

Step2: Identify a, b, c values

$a=4,\ b=-32,\ c=64$

Step3: Calculate discriminant $\Delta=b^2-4ac$

$\Delta=(-32)^2 - 4(4)(64) = 1024 - 1024 = 0$

Step4: Interpret discriminant value

A discriminant of 0 means one real rational solution.

Answer:

One real, rational