Question

Which of the following describes the root(s) of the equation (9x² = 6)?

a) Exactly one real root
b) Two distinct imaginary roots
c) Exactly one imaginary root
d) Two distinct real roots

Answer 1

The given equation 9x² = 6 is a quadratic equation which, after simplification and using the discriminant, shows that it has two distinct real roots.

Step-by-step explanation:

The equation in question is a quadratic equation of the form ax² + bx + c = 0, where a, b, and c are constants. For the given equation 9x² = 6, we first need to bring it to the standard form by subtracting 6 from both sides, giving us 9x² - 6 = 0.

Dividing the entire equation by 3 we get 3x² - 2 = 0, which is now in standard form ax² + bx + c = 0 with a = 3, b = 0, and c = -2. Now we can determine the number and type of roots using the discriminant b² - 4ac. In this case, the discriminant is 0² - 4(3)(-2) = 24, which is positive, indicating that there are two distinct real roots.

Therefore, the correct answer is d) Two distinct real roots.