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Question

# If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then f(x)=0 has

A
4 real roots
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B
5 real roots
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C
3 real roots
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D
nothing can be said
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Solution

## The correct option is B 5 real rootsGiven, f(|x|)=0 has 8 real roots⇒f(√x2)=0 has 8 real roots⇒f(x)=0 has 4 positive roots.Since, f(x) is a polynomial of odd degree.So,f(x) cannot have even number of real roots .And since, total number of roots are 5, so one root will be negative.So, f(x)=0 has all five roots real.

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