Question

If α, β, γ are the zeroes of the cubic polynomial 4x3 + 8x2 – 6x – 2 then find αβγ.​

Answer 1

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We know that for the equation,

ax³+bx²+cx+d = 0

α+β+γ = -b/a

αβ+βγ+γα = c/a

αβγ = -d/a

Hence in the given equation

4x³+8x²-6x-2 = 0

a= 4

b = 8

c = -6

d = -2

Hence

αβγ = -d/a

αβγ = -(-2)/4

αβγ = 2/4 = 1/2

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