Paragraph question...

If f(x)=3x3-13x2+14x-2 and p,q,r are roots of f(x)=0 such that p<q<r,then

1),[q],[r] where [.] denotes greatest integer function,are in

A)A.P
B)G.P
C)H.P
D)A.G.P

2)\fn_jvn \lim_{n\rightarrow \infty }(p)^{n!}(q)^{1/n} =

A)0
B)1
C)e
D)e2

4 Answers

333
Hardik Sheth ·

expression is always negative for negative x.f(0)=-2.f(1)=2.=>box p=0.
again,f(2) is negative.box q=1.f(3)is positive.box r=2.
therefore in AP,i suppose.

333
Hardik Sheth ·

ans 2 is 0

1057
Ketan Chandak ·

sorry...the first question is (box)(p),[q],[r].Actually the p doesn't work in boxes as it denotes power.. :P

333
Hardik Sheth ·

no need to find the roots...differentiate once...check roots of f'(x).between two roots,we have one root of f(x).see where sign is changing and you just need the box of it..so its easy.

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