Question

Determine the nature of the roots: 3x^2+12x-3=0

two distinct real solutions

c.

no real solutions
b.

cannot be determined

d.

a unique real solution

Answer 1

The answer is C)

two distinct real solutions

Explanation:

On edge 2021

Answer 2

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+12x-3=0 \\ \\ a=3 \\ b=12 \\ c=-3 \\ \\ \Delta=b^2-4ac=12^2-4 * 3 * (-3)=144+36=180`

Δ>0, so there are two distinct real solutions. The answer is A.