Question

if alpha beta and gamma are the zeros of polynomial ax³+bx²+54x+3, then find the value of alpha×beta+beta×gamma+gamma×alpha.​

Answer 1

Answer: 1

Step-by-step explanation:We have a 3 degree polynomial here of form

ax³ + bx² + cx +d = 0

Polynomial p(x) = 3x³ + 6x² + 5x - 3 = 0

The roots of this polynomial are α, β, γ

We have formula for sum and products of zeroes as

Sum of roots = α + β + γ = -b/a

α + β + γ = -(-6)/3 = 2

α + β + γ = 2

And product of roots is given by

Product taking 2 at a time = αβ + βγ + αγ = c/a

αβ + βγ + αγ = 5/3

Product taking 3 at a time = αβγ = -d/a

αβγ = -(-3)/3 = 1