Question

Use the discriminant to describe the roots of each equation. Then select the best description. 2x2 + 7x + 6 = 0 real and irrational roots real and rational roots double root non-real roots

Answer 1

roots are real and rational

Explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is

b² - 4ac

the discriminant informs on the nature of the roots

• if b² - 4ac > 0 then roots are real and irrational

• if b² - 4ac > 0 and a perfect square, then roots are real and rational

• if b² - 4ac = 0 , then roots are real and equal

• if b² - 4ac < 0 , then the roots are not real

for 2x² + 7x + 6 = 0 , in standard form

with a= 2, b = 7 , c = 6 , then

b² - 4ac = 7² - (4 × 2 × 6) = 49 - 48 = 1

since b² - 4ac > 0 and a perfect square, then the roots are real and rational