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If f(x) =ax^(2) +bx + c, g(x)= -ax^(2...

If ` f(x) =ax^(2) +bx + c, g(x)= -ax^(2) + bx +c " where " ac ne 0 " then " f(x).g(x)=0` has

A

our real roots

B

Two real roots

C

Four imaginary roots

D

None of these

Text Solution

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The correct Answer is:
B
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Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .