Question

Determine the number of possible positive and negative real roots of the equation:

x - 4x + 5x² + 9x² + 2x 8
a 2 or 0 negative roots; 3 or 1 positive roots
b. 5, 3, or 1 negative roots;
4, 2 or 0 positive roots
c.
d.
2 or 1 neative roots; 3 or 2 positive roots
3 or 1 negative roots; 2 or 0 positive roots

Answer 1

The given equation has two positive roots and zero negative roots.

Step-by-step explanation:

The given equation is x - 4x + 5x² + 9x² + 2x - 8 = 0. To determine the number of possible positive and negative real roots, we need to use the discriminant of the quadratic equation. The discriminant is the part inside the square root of the quadratic formula.

In this case, a = 5, b = -4, and c = -8. Substituting these values into the discriminant formula, we get:

discriminant = b² - 4ac = (-4)² - 4(5)(-8) = 16 + 160 = 176.

Since the discriminant is positive (176 > 0), there are two positive roots and zero negative roots.