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Question

Let , f(x)=ax2+bx+c, g(x)=ax2+px+q where a,b,c,q,p, ϵ R and b  p. If their discriminants are equal and f(x) = g(x) has a root , α then



A

will be A.M. of the roots of f(x) = 0, g(x) = 0

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B

will be G.M of all the roots of f(x) = 0, g(x) = 0

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C

will be A.M of the roots of f(x) = 0 or g(x) = 0

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D

will be G.M of the roots of f(x) = 0 or g(x) = 0

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Solution

The correct option is B

will be A.M. of the roots of f(x) = 0, g(x) = 0


aα2+bα+c=aα2+pα+qα=qcbp(i)And b24ac=p24aqb2p2=4a(cq)b+p=4a(cq)bp=4aα        (from (i))

α=(b+p)4a=bapa4 which is A.M of all the roots of f(x) = 0 and g(x) = 0


Mathematics

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