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Let f(x)=a5x^5+a4x^4+a3x^3+a2x^2+a1x , w...

Let `f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x ,` where `a_i ' s` are real and `f(x)=0` has a positive root `alpha_0dot` Then `f^(prime)(x)=0` has a positive root `alpha_1` such that `0

A

f'(x) = 0 has a root `alpha_(1) "such that"ltalpha_(1)ltalpha_(0)`

B

f' (x) = 0 has at least one real root

C

f''(x) = 0 has at least one real root

D

none of these

Text Solution

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The correct Answer is:
A, B, C
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