Question

Use the discriminant of quadratic equations, b²-4ac, to determine whether the following functions have two real roots, one real root, or two complex roots. a) for f(x)=2x²-12x+18: since b²-4ac is the discriminant, it has

1) two real roots
2) one real root
3) two complex roots

Answer 1

The quadratic function f(x) = 2x² - 12x + 18 has one real root, as the discriminant b² - 4ac is zero.

Step-by-step explanation:

To determine whether the quadratic function f(x) = 2x² - 12x + 18 has two real roots, one real root, or two complex roots, we must use the discriminant of quadratic equations, b² - 4ac. For this function, a = 2, b = -12, and c = 18. Plugging these values into the discriminant formula we get:

Discriminant = b² - 4ac = (-12)² - 4(2)(18) = 144 - 144 = 0.

Since the discriminant is zero, it means the quadratic equation has one real root. This is because when the discriminant is positive, there are two real roots; when it's zero, there is exactly one real root (a repeated root); and when it's negative, there are two complex roots.