Question

If α and β (≠ 0) are the roots of the quadratic equation x2 + αx - β = 0, then the quadratic expression -x2 + αx + β where x ∈ R has

a. Least value - 1/4

b. Least value - 9/4

c. Greatest value 1/4

d. Greatest value 9/4

Answer 1

Correct option d. Greatest value 9/4

Explanation:

α + β = - α, αβ = - β ⇒ αβ + β = 0

⇒ (α + 1)β = 0 ⇒ α = - 1 (β ≠ 0)

⇒ 2α + β = 0

⇒ β = 2

∴ -x2 + x + = - x2 - x + 2

Greatest value = - (1 + 8)/-4 = 9/4