Use the discriminant to describe the roots of each equation. then select the best description. x^2 + 9x + 14 = 0 a) double root b) real and rational roots c) real and irrational roots d) non-real roots

B

given a quadratic equation in standard form

ax² + bx + c = 0

Then we can describe the nature of the roots using the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0, then 2 real, distinct and irrational roots

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

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

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

for x² + 9x + 14 = 0

with a = 1, b= 9 and c = 14, then

b² - 4ac = 9² - (4 × 1 × 14 ) = 81 - 56 = 25

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