Question

use the discriminant to describe the roots of each equation. Then select the best description. 2m^2+3=m

Answer 1

roots are not real

Explanation:

given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

then the discriminant Δ = b² - 4ac

the value of the discriminant informs us about the nature of the roots

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

• If b² - 4ac = 0, then 2 real and equal roots

• If b² - 4ac < 0, then no real roots

given 2m² + 3 = m ( subtract m from both sides )

2m² - m + 3 = 0 ← in standard form

with a = 2, b= - 1 and c = 3

b² - 4ac = (- 1)² - (4 × 2 × 3) = 1 - 24 = - 23

Since b² - 4ac < 0 the equation has no real roots