Question

find a Cubic bolynomial with the Sum Sum of the product of its zeroes and product of its zeroes are 5,-6,and -20​

Answer 1

Answer:

find a Cubic bolynomial with the Sum Sum of the product of its zeroes and product of its zeroes are 5,-6,and -20

${x}^{3} - (sum \: of \: zeros) {x}^{2} + sum \: of \: \\ product \: of \: zerosx \: - product \\ of \: zeros$

${x}^{3} - 5 {x}^{2} - 6x + 20$

hope it helps!!

Answer 2

Answer:-

${x}^{3} - 5x^2 - 6x + 20$

Given :-

$\alpha +\beta+\gamma = 5$

$\alpha \beta + \beta \gamma + \gamma \alpha = - 6$

$\alpha \beta \gamma = - 20$

To find :-

The required cubic polynomial.

Solution :-

Cubic polynomial :- The polynomial whose highest degree is 3 is known as cubic polynomial.

The required cubic polynomial is given by :-

$= > {x}^{3} - ( \alpha + \beta + \gamma ) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - ( \alpha \beta \gamma )$

Now, put the given value :-

$= > {x}^{3} - (5) {x}^{2} + ( - 6)x - (20)$

$= > {x}^{3} - 5 {x}^{2} - 6x + 20$

hence, the required cubic polynomial is

${x}^{3} - 5x^2 - 6x + 20$