Question

use the discriminant to answer the questions.
12x - 4 - 4x² = 0
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

First, rewrite the equation $32x - 4 - 4x^2 = 0$ in $ax^2+bx+c=0$ form:
$$-4x^2 + 32x - 4 = 0$$
We can simplify by dividing by $-4$:
$$x^2 - 8x + 1 = 0$$
Here, $a=1$, $b=-8$, $c=1$.

Step2: Calculate the discriminant

Use discriminant formula $\Delta = b^2 - 4ac$:
$$\Delta = (-8)^2 - 4(1)(1) = 64 - 4 = 60$$

Step3: Analyze the discriminant

$\Delta=60>0$, so there are two real solutions. Since 60 is not a perfect square, the solutions are irrational.

Answer:

Two real, irrational