Question

Find a a polynomial having zeros `-6,-4,3,7` and coefficient of highest degree as `1`?

Answer 1

`x^4-55x^2-30x+504=0`

Explanation:

A polynomial having zeros `alpha,beta,gamma,delta` and coefficient `a` can be constructed as

`a(x-alpha)(x-beta)(x-gamma)(x-delta)=0`

Hence, a polynomial having zeros `-6,-4,3,7` and coefficient `1` can be written as

`(x-(-6))(x-(-4))(x-3)(x-7)=0`

or `(x+6)(x+4)(x-3)(x-7)=0`

or `(x^2+10x+24)(x^2-10x+21)=0`

or `x^4-10x^3+21x^2+10x^3-100x^2+210x+24x^2-240x+504=0`

or `x^4-55x^2-30x+504=0`