Question

if alpha beta and gamma are the zeros of the cubic polynomial p(x)= 3x^3-6x^2+5x-3,then find their sum and product

Answer 1

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

Answer 2

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