Question

find a cubic polynomial with the sum sum of the product of its zeros taken two at a time, and the product of its zeros as -3, -8, and 2 respectively.

Answer 1

this is your answer ........

Answer 2

Answer:

Required Cubic Polynomial is k ( x³ + 3x² - 8x - 2 )

Step-by-step explanation:

Given:

Sum of the zeroes of the cubic polynomial = -3

Sum of the product of its zeros taken two at a time = -8

Product of the zeroes = 2

To find: The cubic Polynomial.

We know that,

if $\alpha\:,\:\beta\:,\:\gamma$ are zeroes of the polynomial then,

Cubic polynomial is given by,

$k(x^3-(\alpha+\beta+\gamma)x^2+(\alpha\beta+\beta\gamma+\gamma\alpha)x-(\alpha\beta\gamma))$

So, the required cubic polynomial = k ( x³ - (-3)x² + (-8)x - 2 )

                                                         = k ( x³ + 3x² - 8x - 2 )

Therefore, Required Cubic Polynomial is k ( x³ + 3x² - 8x - 2 )