Question

Find a cubic polynomial with the sum , sum of the product of its zeros taken two at a time , and the product of its zeros as 2 , -7, -14 respectively

Answer 1

2x+y=11 and 3x-4/4 a d 2x+y=11

Answer 2

As We know that the cubic polynomial can be ax³+bx²+cx+d and the values of the zeroes of the polynomials be α, β, γ.

As We also know the different relations b/w the zeroes of the Polynomial.

→ α+β+γ = -b/a

→ α+β+γ = 2/1

→ αβ +βγ+γα = c/a

→ αβ +βγ+γα = –7/1

→ αβγ = -d/a

→ αβγ = –14/1

So now we got the values of coefficient of polynomial.

• a = 1, b = -2, c = -7, d = 14

Hence,

The cubic polynomial will be x³–2x²–7x+14.