Question

If alpha beta gamma are zeros of cubic polynomial ax cube+bx square+cx+d=0 then the values of AlphaXbetaXgamma is

Answer 1

value of αβγ = -d/a

it is given that, α, β and γ are zeroes of cubic polynomial, ax³ + bx² + cx + d = 0

sum of zeroes = - coefficient of x²/coefficient of x³

⇒α + β + γ = -b/a

sum of products of two consecutive zeroes = coefficient of x/coefficient of x³

⇒αβ + βγ + γα = c/a

product of zeroes = - constant/coefficient of x³

⇒αβγ = -d/a

hence, αβγ = -d/a

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Answer 2

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