If V3 and - V3 are the zeroes of a polynomial p(x), then find p(x).
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Let α,β,γ zeros of the given polynomial p(x).
It is that product of two zeros of p(x) is 3
ie αβ=3 ________ (1)
Here p(x)=x
3 −6x 2 +11x−6 is of the form ax 3 +bx 2 +cx+d
∴a=1,b=−6,c=11,d=−6Now, αβγ= a−d
⇒αβγ=6
⇒γ= αβ6
⇒γ= 3/6
[from (1)]⇒γ=2
Hence the third zero is 2.
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