Question

Find a cubic polynomial with the sum, sum of the products of its zeroes (two at a time), and product of its zeroes as 14, 1 and  −16 respectively.​

Answer 1

Answer:

x3−2x2−7x+14

Step-by-step explanation:

Let the polynomial be ax3+bx2+cx+d and the zeroes be α,β,γ.

Sum of the polynomial = α+β+γ=12=a−b

Sum of the product of its zeroes taken two at a time = αβ+βγ+αγ=1−7=ac

Product of the root = αβγ=1−14=a−d

If a=1,b=−2,c=−7,d=14.

Hence the polynomial is  x3−2x2−7x+14