Question

Find a polynomial of the specified degree that satisfies the given conditions.

Degree 4;    zeros −3, 0, 1, 5;    coefficient of x³ is 6

Answer 1

Let the polynomial of degree 4 and -3,0,1,5 as zeros be :

i.e.,

i.e.,

i.e.,

i.e.,

Here, the coefficient of x³ is 6.

Then by condition we have,

i.e.,

i.e.,

Then, the polynomial becomes :

i.e.,

Therefore, the required polynomial is : .