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Question

# If f : D →R f(x)=x2+bx+cx2+b1x+c1, where α, β are th roots of the equation x2+bx+c=0 and α1, β1 are the roots of x2+b1x+c1=0. Now, answer the following question for f(x). A combination of graphical and analytical approach may be helpful in solving these problems. If α1 and β1 are real, then f(x) has vertical asymptote at x=(α1, β1). If the equations x2 + bx + c = 0 and x2+b1x+c1=0 do not have real roots, then

A

f'(x) = 0 has real and distinct roots

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B

f'(x) = 0 has real and equal roots

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C

f'(x) = 0 has imaginary roots

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D

nothing can be said

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Solution

## The correct option is A f'(x) = 0 has real and distinct roots f(x) has one of the two graphs ⇒ f'(x) = 0 has real and distinct roots.

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