a, b, c are real numbers. The quadratic equation ax²−bx+c=0 has equal roots, β. Then:
Options:
(A) β = b/a
(B) β² = ac
(C) β³ = bc/(2a²)
(D) b² ≠ 4ac
Official Answer Key:
C
Step-by-Step Solution & Explanation
Equal roots ⇒ β = b/(2a) (sum of roots = b/a = 2β) and β² = c/a (product of roots). So β³ = β·β² = [b/(2a)]·[c/a] = bc/(2a²). (Option A is only β=b/2a, not b/a, so it's incorrect as written; discriminant must equal zero, b²=4ac, ruling out D.)
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