Question

HALPPPP!! Which of the following describes the root(s) of the equation 9x^2 = 6x - 1?

A. Exactly one real root
B. Two distinct imaginary roots
C. Exactly one imaginary root
D. Two distinct real roots

Answer 1

The roots of the equation 9x^2 = 6x - 1 are described by exactly one real root, as the discriminant of the equation is zero, indicating the two roots are the same, forming a perfect square trinomial.

Step-by-step explanation:

To determine which of the following describes the roots of the equation 9x^2 = 6x - 1, we need to rewrite it in the standard quadratic form ax^2 + bx + c = 0. Subtract 6x and add 1 to both sides to get 9x^2 - 6x + 1 = 0. Now, to identify the nature of the roots, we can use the discriminant, which is part of the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), where the discriminant is b^2 - 4ac. For our equation, a = 9, b = -6, and c = 1. Plugging these values into the discriminant gives us (-6)^2 - 4(9)(1) = 36 - 36 = 0.

Since the discriminant equals zero, it indicates that there is exactly one real root. This is because the discriminant being zero means that the two roots are the same, which is a condition known as a perfect square trinomial.