Question

Which two values of x are roots of the polynomial below:

3x^2 - 3x + 1?

A. x = 3 - 28/6
B. x = -3
C. x = 187/128
D. x = -8 + 28/6
E. x = 3 - 1 - 3/6
F. x = 3 + 3/6

Answer 1

The quadratic polynomial 3x^2 - 3x + 1 has no real roots, as the discriminant (b^2 - 4ac) is negative, leading to an imaginary number when using the quadratic formula.

Step-by-step explanation:

The student is asking about the roots of the polynomial 3x2 - 3x + 1. To find the roots, we use the quadratic formula:

x = ∛(-b ± √(b2 - 4ac)) / (2a)

In this equation, a = 3, b = -3, and c = 1. Plugging these values into the quadratic formula, we get:

x = ∛(-(-3) ± √((-3)2 - 4(3)(1))) / (2(3))

Simplifying further:

x = ∛(3 ± √(9 - 12)) / 6

Since 9 - 12 is negative, we end up with an imaginary number which means the polynomial has no real roots.