Question

How many roots and of what type for this quadratic equation?

9n² −3n−8=−10
A) 2 real roots
B) 2 complex roots
C) 1 real root
D) 1 complex root

Answer 1

The quadratic equation has 2 real roots. The correct option is A).

Step-by-step explanation:

The given quadratic equation is 9n² - 3n - 8 = -10.

To determine the number and type of roots, we can compare the equation with the standard form of a quadratic equation ax² + bx + c = 0.

In this case, a = 9, b = -3, and c = -8 - (-10) = -2.

Using the discriminant formula, D = b² - 4ac, we have D = (-3)² - 4(9)(-2) = 9 + 72 = 81.

Since the discriminant is positive (D > 0), the quadratic equation has 2 real roots.

Therefore, the correct answer is Option A) 2 real roots.