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Differential Calculus

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31 Dec 2011 01:23:47 IST

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FUNCTIONS: COMPREHENSION

Mathematics

p(x) be polynomial of dgree atmost 5

which leaves remainder -1 and +1

upon division by (x-1)^3 and (x+1)^3 respectively.

Q1-no. of real roots of p(x):

a)1 b)2 c)3 d)5

Q2-the max value of y=p' '(x) can be obtained at x=

a) -1/root3 b)0 c) 1/root3 d)1

Q3-the sum of pairwise product of all

the roots (real and complex) of p(x)=0 is:

a) -5/3 b)-10/3 c)2 d) -5

-ROHIT KUMAR RAJPOOT

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AGNIPROBHO MAZUMDER

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8 Feb 2012 21:09:56 IST

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FUNCTIONS: COMPREHENSION

AGNIPROBHO MAZUMDER

New kid on the Block

Joined: 14 Oct 2011

Posts: 4

9 Feb 2012 14:23:47 IST

Like 1 people liked this

p(x)=(Ax² + Bx + C)(x+1)³ + 1 ……………………..<i>

p(x)=(Dx² + Ex +F)(x-1)³ – 1 ………………………….<ii>

Equating <i> & <ii> , we get 6 equations:- A=D ; C+1=-F-1 ; 3A+B=E-3D ; 3A+3B+C=3D-3E+F ;

3E-D-3F=A+3B+3C ; 3F-E=B+3C

Solving, we get A=-3/8 ; B=9/8 ; C=-1 ; D=-3/8 ; E=-9/8 ; F=-1

Hence p(x)=(-3/8)x⁵ +(5/4) x³ +(-15/8)x

p(x) has only one real root x=0

p”(x)=(-15/2)(x³ – x) has a maximum at x=1/√3

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