Question

Determine the nature of the roots:

Answer 1

A

Explanation:

Nature of roots is determined by using the Discriminant, D, which is:

`D=b^2-4ac`

If

D > 0, there are 2 real unique solutions

D = 0, there are 2 real equal solutions

D < 0, there are no real solutions

Note: a is the coefficient of x^2, b is the coefficient of x, and c is the independent term (the constant)

Now, for our quadratic expression, a = 3, b = 12, & c = -3. Plugging it in the discriminant formula, we get:

`D=b^2-4ac\\D=(12)^2-4(3)(-3)\\D=180`

Thus, D > 0 , which means there are 2 distinct real solutions. Answer choice A is right.