Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2,-7,-14 respectively?
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Answer:
Let the polynomial be ax
3
+bx
2
+cx+d and the zeroes be α,β,γ.
Sum of the polynomial = α+β+γ=
1
2
=
a
−b
Sum of the product of its zeroes taken two at a time = αβ+βγ+αγ=
1
−7
=
a
c
Product of the root = αβγ=
1
−14
=
a
−d
If a=1,b=−2,c=−7,d=14.
Hence the polynomial is x
3
−2x
2
−7x+14
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