Question:
find a cubic polynomial with the sum, sum of its products of its zeroes taken two a time and the product of its zeroes as -3 , -8 and 2 respectively.
Answer:
Let three zeroes a, b ,c
Now given a+b+c = -3
ab+bc+ca = -8
abc = 2
Now cubic equation is
x3 - (a+b+c)x2 + (ab+bc+ca)x - abc= 0
=> x3 + 3x2 - 8x - 2 =0
So the required equation is: x3 + 3x2 - 8x - 2 =0
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