Question

find a cubic polynomial with the sum Sum of the product of its zeros taken two at a time and product of its zero,5, - 6 and - 20 respectively

Answer 1

I hope it will help you

Answer 2

Answer: Required cubic polynomial is $x^3-5x^2-6x+20$

Step-by-step explanation:

Since we have given that

Sum of zeroes of a cubic polynomial is given by

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

Sum of the product of its zeroes taken two at a time is given by

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

Product of its zeroes is given by

$\alpha\beta  \gamma=-20$

As we know the formation of cubic polynomial :

$x^3-(\text{Sum of zeroes})x^2+(\text{Sum of product of its zeroes taken two at a time})x-\text{Product of its zeroes}=0\\\\=x^3-5x^2-6x+20$

Hence, required cubic polynomial is $x^3-5x^2-6x+20$