Question

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x= 2 andx = 0, and a root of multiplicity 1 at x=-4Find a possible formula for P(x).

Answer 1

We know that we can write the equation in the form

P(x) = a(x-b1) (x-b2) (x-b3)...... where b1,b2,.... are the roots

When we have a multiplicity greater than 1, we take the (x-b) to that power

a is the leading coefficient

p(x) = 1(x-2)^2 (x-0)^2 (x - -4)

Simplifying

P(x) = (x-2)^2 *x^2 * (x+4)

P(x) = x^2 ( x-2)^2 (x+4)