Question

Find a cubic polynomial with sum,sum of its products of its zeroes taken two at a time and the product of its zeroes is 5,-6 and -20 respectively

Answer 1

Given:

In a cubic polynomial:

• Sum of Zeroes= 5
• Sum of products of zeroes taken two at a time= -6
• Product of Zeroes= -20

To Find:

• Cubic Polynomial

Solution:

We know that, cubic polynomial is expressed in the form of

p(x)= x³-(S)x²+(T)x-P

where,

S= Sum of Zeroes

T= Sum of product of zeroes taken two at a time

P= Product of Zeroes

x is any variable

Now,

Required polynomial is

p(x)= x³-(5)x²+(-6)x-(-20)

p(x)= x³-5x²-6x+20

Some Important Facts:

For a cubic polynomial,

p(x)= ax³+bx²+cx+d

$\sf{Sum\:of\:Zeroes= -\dfrac{Coefficient\:of\:x^{2} }{Coefficient\:of\:x^{3}}}$

$\sf{Sum\:of\:product\:of\:Zeroes\:taken\:two\:at\:a\:time= \dfrac{Coefficient\:of\:x }{Coefficient\:of\:x^{3}}}$

$\sf{Product\:of\:Zeroes= -\dfrac{Constant\:term}{Coefficient\:of\:x^{3}}}$

Answer 2

Given:

In a cubic polynomial:

Sum of Zeroes= 5

Sum of products of zeroes taken two at a time= -6

Product of Zeroes= -20

To Find:

Cubic Polynomial

Solution:

We know that, cubic polynomial is expressed in the form of

p(x)= x³-(S)x²+(T)x-P

where,

S= Sum of Zeroes

T= Sum of product of zeroes taken two at a time

P= Product of Zeroes

x is any variable

Now,

Required polynomial is

p(x)= x³-(5)x²+(-6)x-(-20)

p(x)= x³-5x²-6x+20