Question

Find the cubic polynomial whose zeroes are 3,-1
and -1/3.​

Answer 1

Step-by-step explanation:

cubic Eqn. Is of the form...

cubic Eqn. Is of the form...

We have three unknowns a,b,c and so we need 3 Eqns.. Which are as follows..

Eqn. 1

When 3 is a zero of polynomial eqn

27+9a+3b+c=0

Eqn. 2

When - 1/2 is a zero

-1/8+1/4a-1/2b+c=0 or

-1+2a-4b+8c=0

Eqn. 3

When - 1 is a zero

-1+a-b+c=0

On simplifying these three equations, you'll get

a= - 5/2

b= - 2

c= 3/2

So, polynomial equation becomes

therefore,

Eqn finally becomes