Question

Determine the nature of the roots: 3X^2-6X+3=0
a.

a unique real solution

c.

cannot be determined
b.

two distinct real solutions

d.

no real solutions

Answer 1

The roots of a quadratic equation ax²+bx+c=0 can be determined by calculating the discriminant Δ=b²-4ac.
If Δ>0, there are two distinct real solutions.
If Δ=0, there is one real solution.
If Δ<0, there are no real solutions and two complex solutions.

$3x^2-6x+3=0 \\ \\ a=3 \\ b=-6 \\ c=3 \\ \\ \Delta=b^2-4ac=(-6)^2-4 \times 3 \times 3=36-36=0$

Δ=0, so there is one real solution. The answer is A.

The solution is:
$x=\frac{-b}{2a}=\frac{-(-6)}{2 \times 3}=\frac{6}{6}=1$