Question

Use the discriminant to describe the roots of each equation. Then select the best description.

Answer 1

The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).

How to determine the characteristics of the roots of a quadratic equation by discriminant

Herein we have a quadratic equation of the form a · x² + b · x + c = 0, whose discriminant is:

d = b² - 4 · a · c     (1)

There are three possibilities:

1. d < 0 - conjugated complex roots.
2. d = 0 - equal real roots (real and rational root).
3. d > 0 - different real roots (real and irrational root).

If we know that a = 3, b = 7 and c = - 2, then the discriminant is:

d = 7² - 4 · (3) · (- 2)

d = 49 + 24

d = 73

The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).

To learn more on quadratic equations: brainly.com/question/2263981

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