11Ans 4) http://targetiit.com/iit-jee-forum/posts/quady-ractic-12693.html
Q1 Find the no. of rational and irrational roots of x^3+1=2(2x-1)^{1/3}
Q2 Let P(x) be a polynomial such that P(x^2+2)=x^{17}-3x^5+x^3-3 then find roots of P(x)
Q3 Let a,b,c ε R and a≠0 be such that (a+c)2<b2 the nfind no. of roots of eqn ax2+bx+c=0
Q4 Maximise y=2(a-x)(x+√x2+b2)
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62Eureka are you sure question 2 is this?
Shouldnt a polynomial in x2 should have all coefficients of x as even!
62q3)
look at (a+b+c)(a-b+c) < 0
so f(1).f(-1)<0
so it has 2 real roots
62Q1) is of the form f(x) = f-1x
By the form of f(x), we can say that all real roots will be when f(x) = x
so you have to solve x3+1=x
this will not have any rational roots..
x(1-x2) = 1
1-(p/q)2 = q/p
so (q2-p2)p = q
but p and q are coprime so lhs is not a multiple of q .. hence no rational root.
also it will have exactly 1 real (irrational) root because of the graph.
24yes sir Q2 si rite...and now i understand why ans is given "No such polynomial exists"[1]
24in Q1
f(x) =x3+12 naa ?
so we should solve x3+12=x naa ???
rather than x3+1=x
