Question

If a cubic polynomial with the sum of its zeroes, sum of the products and its zeroes taken two at a time an product of its zeroes as 2, -5 and -11 respectively, then the cubic polynomials is ?​

Answer 1

Answer:

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 = 

$αβγ=1−14=a−d</p><p>If a=1,b=−2,c=−7,d=14.$

Hence the polynomial is  x3−2x2−7x+14