Question

HELP PLEASE
Use the value of the discriminant to determine the number and type of roots for the equation,
X^2 = 4x - 4
A. 2 real, irrational roots
B. 1 real, rational root
C. 2 complex roots
D. 2 real, rational roots

Answer 1

We are given –

$\qquad$ $\twoheadrightarrow\bf x² = 4x -4$

$\qquad$ $\twoheadrightarrow\bf x² -4x +4 = 0$

• Where, a = 1 ; b = -4 ; c = 4

Let's find it's discriminant.

We know –

$\qquad$ $\purple{\twoheadrightarrow\bf Discriminant = b² - 4ac}$

$\qquad$ $\twoheadrightarrow\sf Discriminant = (-4)² - 4 \times 1 \times 4$

$\qquad$ $\twoheadrightarrow\sf Discriminant = 16-16$

$\qquad$ $\purple{\twoheadrightarrow\sf Discriminant =0 }$

• If Δ (Discriminant) >0here are two separate real roots.
• If Δ (Discriminant) =0, there are two identical real roots.
• If Δ (Discriminant) <0, there are no real roots, but there are two complex roots.

As we got –

• Δ Discriminant is 0 that means , there are two identical real roots. Henceforth, Option (D) 2 real, rational roots – is correct.