TargetIIT

Let [im]http://codecogs.izyba.com/gif.latex?P%28x%29%3Dx%5E5+ax%5E4+bx%5E3+cx%5E2+dx+e[/im].
If the graph of y = P(x) cuts the x-axis at five distinct points and P(0)=0, then which of the coefficients cannot be zero?

is it c???

[im]http://codecogs.izyba.com/gif.latex?P%280%29%3D0%20%5C%5C%20means%20%5C%20e%20%3D0%20%5C%5C%20x%28ax%5E4+.......%20%29%20%5C%5C%20since%5C%20there%20%5C%20are%20%5C4%20%5C%20roots%20%5C%20of%20%5C%20the%20%5C%20residual%20%5C%20polynomial%20%5C%20equation%20%5C%20it%20%5C%20must%20%5C%20be%20%5C%204th%20%5C%20degree%20%5C%20%5C%5C%20hence%20%5C%20a%20%5C%20cannot%20%5C%20be%20%5C%200[/im]

@arshad, no its not c

@;) the factorization should be x(x[p]4[/p] + ax[p]3[/p] + ...)

oh sorry sir
P(x)=x.(x-α)(x-β)(x-γ)(x-δ)
NOW AS ALL ROOTS ARE DISTINCT
α,β,γ,δ NONE OF THEM CAN BE 0
HENCE α.β.γ.δ ≠0
HENCE d≠0

How does d≠0 guarantee that all roots are real and distinct ?

you are reversing the claim: he's proving p→q and you are asking about q→p