Question

find cubic polynomial with the sum Sum of the product of its zeros taken two at a time and the productor 0 as 2, - 7 -14​

Answer 1

Question:

Find a cubic polynomial whose sum of zeros,product of zeros taken twice and product of zeros is 2,-7 and -14 respectively.

Solution:

Let a,b and c be the zeros of the required cubic polynomial

Given that,

a+b+c=2

ab+bc+ac= -7

and,abc= -14

Required Polynomial:

x³+(a+b+c)x²-(ab+bc+ac)x+abc

=x³+2x²+7x-14

Hence,p(x)=x³+2x²+7x-14

Answer 2

Answer:

p(x)=x³+2x²+7x-14

Explanation:

Given Problem:

Find cubic polynomial with the sum Sum of the product of its zeros taken two at a time and the productor 0 as 2, - 7 -14​

Solution:

To Find:

Cubic polynomial.

-------------------------

Method:

Let x,y and z be the zeros of the cubic polynomial.

According to your question:

$\sf x+b+z=2\\\\\ \xy+yz+xz= -7\\\\ \xyz= -14$

Now,

Cubic polynomial:

$\sf x^3+(x+y+z)x^2-(xy+yz+xz)x+xyz\\\\ =>x^3+2x^2+7x-14$

$\bigstar\sf Hence, It\;implies\;that\;the\;cubic\;polynomial\;is\;p(x)=x^3+2x^2+7x-14\bigstar$