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प्रश्न
If the equation (1 + m2) x2 + 2cm x + c2 − a2 = 0 has repeated roots then the correct relation is ______.
पर्याय
c2 = a2 (1 + m2)
a2 = c2 (1 + m2)
c2 + a2 (1 + m2) = 0
a2 + c2 (1 + m2) = 0
MCQ
रिकाम्या जागा भरा
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उत्तर
If the equation (1 + m2) x2 + 2cm x + c2 − a2 = 0 has repeated roots then the correct relation is c2 = a2 (1 + m2).
Explanation:
Given:
(1 + m2) x2 + 2 cmx + (c2 − a2) = 0
Ax2 + Bx + C = 0, repeated roots occur when:
Δ = B2 − 4AC = 0
A = 1 + m2, B = 2 cm, C = c2 − a2
(2 cm)2 − 4(1 + m2) (c2 − a2) = 0
4c2m2 − 4(1 + m2) (c2 − a2) = 0
Divide by 4:
c2m2 − (1 + m2) (c2 − a2) = 0
c2m2 − (c2 − a2) − m2(c2 − a2) = 0
a2(1 + m2) − c2 = 0
c2 = a2(1 + m2)
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