Question:
Find a cubic polynomial with the sum,sum of the product of its zeroes taken two at a time & the product of its zeroes are 3,0,-4
Answer:
Let a, b, c are the zeroes of the cubic polynomial.
Given a + b + c = 3
a*b + b*c + c*a = 0
and a*b*c = -4
Now, the cubic polynomial = x3 - (a + b + c)x2 + (a*b + b*c + c*a)x - a*b*c
= x3 - 3x2 + 0*x - (-4)
= x3 - 3x2 + 4
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