Question

X2 - 4x + 4 = 0

Use the discriminant to describe the roots of each equation. Select the best description.
A) non-real roots
B) double root
C) real and rational roots
D) real and irrational roots

Answer 1

B, a double root

Explanation:

for a quadratic equation ax²+bx+c=0,

we define the discriminant as:

D=b²-4ac

if D=0, we have a double root

if D>0, we have real roots (is D is a square of an integer, they are also rational

if D<0, we get non-real roots.

this derives from the formula to solve the equation, where D appears in a root:

X1,2= (-b±sqrt(D))/a

in the given equation, a=1, b=-4, c=4, so we get:

D = (-4)²-4×1×4 = 0

hence the answer is B