Question

If the roots of the equations ax² + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then

विकल्प

• b = ac

• b² = ac

• a² = bc

• c² = ab

Answer 1

b² = ac

Explanation:

Given equations have real roots, then

D₁ ≥ 0 and D₂ ≥ 0

(2b)² – 4ac ≥ 0 and `(-2sqrt"ac")^2 - 4"b"."b"` ≥ 0

4b² – 4ac ≥ 0 and 4ac – 4b² ≥ 0

b² ≥ ac and ac ≥ b²

⇒ b² = ac