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 _0. Then

JEE Advanced Mathematics question

Mathematics Application of Derivatives JEE Advanced

Let , where 's are real and has a positive root . Then

(A) has a root such that Correct
(B) has at least one real rootCorrect
(C) has at least two real roots
(D)none of these

Answer: (A),(B)

Solution

(a) ✓: and with . is a polynomial, so by Rolle's theorem there is with . - (b) ✓: follows from (a). - (c) ✗: Counter-example. Take (so ). Then $f(1) = 1 + 1 -

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Question ID VK-109454