Question

If the zeroes of the cubic polynomial are - 2,-3,and - 1 then form a cubic polynomial ​

Answer 1

Answer:

Here, the cubic polynomial is=x^3+2x^2-5x-6=0

Step-by-step explanation:

Let the zeroes be (alpha), (beta), ( gama) respectively.

As here we have to find out a cubic polynomial, So,

Now, find out the sum of the zeroes=(alpha+beta+gama)

=The sum of the product of zeroes=(alpha×beta+beta×gama+gama×alpha)

=Product of the zeroes=(alpha×beta×gama)

Now, after putting the values of these all, we get,

=Sum of zeroes=2+(-3)+(-1)=2-3-1=-2

=Sum of product of zeroes=2×(-3)+(-3)×(-1)+(-1)×2

=(-6)+3+(-2)=3-8=-5

=Product of zeroes=2×(-3)×(-1)=6

Now, as there is considered a formula to find out a cubic polynomial is,

=x^3-(alpha+beta+gama)x^2+(alpha. beta+beta.gama+gama.alpha)x-(alpha.beta.gama)

So, by putting values of all of these, we get,

=x^3-(-2)x^2+(-5)x-6=0

=x^3+2x^2-5x-6=0 is our poynomial.

I hope you would get help by my answer.

Thank you.