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Algebra
Let there be a polynomial with atmost degree 5 such that when divided by (x-1)^3 leaves -1 as the remainder and when divided by (x+1)^3 leaves +1 as the remainder Find :a) No of real roots of P(x) [ans : 1]b) Summation of double product of the roots of P(x) (both real and imaginary) [ans : -5/3]c) Maximum value of "2nd derivative of P(x)"
Comments (5)
the method is a bit lengthy and i m nt sure if it will work bt m tellin u wht i thought
let p(x)=ax^5+bx^4+cx^3+dx^2+ex+f
now we have to find 5 unknowns
since (x-1)^3 gives remainder -1 and (x+1) ^3 gives 1therefore
p(1)=-1 .............1
p(omega)=-1 .........2
p(-1)=1 ..............3
p(-omega)=1 .............4
now compare real and imaginary parts in eq 2 and 4 to get some relations in abcdef and use eq. 1 and 3 to solve for abcdef
i m nt sure if it is correct to use eq 2 and 4
corrections are welcomed
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could someone please answer the question !!!!!