α, β and γ are the Zeroes of Cubic Polynomial P(x) = ax^3 + bx^2 + cx + d, (a≠0). Then Product of their Zeroes [αβγ] is?

α, β and γ are the Zeroes of Cubic Polynomial P(x) = ax³ + bx² + cx + d, (a≠0). Then Product of their Zeroes [αβγ] is?

Solution:

To find the product of the zeroes of a cubic polynomial, we can use Vieta's formulas. Let's denote the cubic polynomial as P(x) = ax³ + bx² + cx + d.

According to Vieta's formulas, the product of the zeroes (zeros) of a cubic polynomial is given by the ratio of the constant term to the coefficient of the highest power of x, with appropriate signs.

In this case, the zeroes are denoted as alpha, beta, and gamma. We know that alpha, beta, and gamma are not equal to 0. Therefore, we can write the product of the zeroes as:

Product of zeroes = (-1)ⁿ * d / a

where n is the number of terms in the polynomial. In this case, n = 3.

So, the product of the zeroes is:

Product of zeroes = (-1)³ * d / a = -d/a

Hence, the product of the zeroes of the cubic polynomial P(x) = ax³ + bx² + cx + d, where alpha, beta, and gamma are the zeroes and not equal to 0, is -d/a.

Answer:

α, β and γ are the Zeroes of Cubic Polynomial P(x) = ax³ + bx² + cx + d, (a≠0). Then Product of their Zeroes [αβγ] is -d/a

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