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If F(X) is a Polynomial Such that F(A) F(B) < 0, Then What is the Number of Zeros Lying Between a and B? - Mathematics

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Question

If f(x) is a polynomial such that f(af(b) < 0, then what is the number of zeros lying between a and b?

True or False

Solution

If  f (x) is a polynomial such that  `f(a) f (b) < 0` then this means the value of the polynomial are of different sign for a to b

Hence, at least one zero will be lying between a and b

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Chapter 2: Polynomials - Exercise 2.4 [Page 61]

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RD Sharma Mathematics [English] Class 10
Chapter 2 Polynomials
Exercise 2.4 | Q 39 | Page 61

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