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:
- d < 0 - conjugated complex roots.
- d = 0 - equal real roots (real and rational root).
- 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: https://brainly.com/question/2263981
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