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 5 ,- 2 and minus -24 respectively

Answer 1

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Answer 2

Answer:

The polynomial is

$x^3-5x^2-2x+24$

Step-by-step explanation:

Given the sum, sum of the product of zeros taken two at a time and the product of its zeros as 5 ,- 2 and minus -24 respectively.

we have to find the polynomial.

$\text{Let }\alpha, \beta, \gamma \text{ are the zeroes of given polynomial}$

$\text{sum of zeroes}=\alpha+\beta+\gamma=5$

$\text{sum of product of zeroes}=\alpha\beta+\beta\gamma+\gamma\alpha=-2$

$\text{Product of zeroes}=\alpha.\beta\gamma=-24$

As the general form of polynomial is

$x^3-(\text{sum of zeroes})x^2+(\text{sum of product of zeroes})x-(\text{Product of zeroes})$

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

$x^3-(2)x^2+(-2)x-(-24)$

$x^3-5x^2-2x+24$

which is required polynomial.