Question

Find a third degree polynomial with the given zeros and a leading coefficient of 4. 1/2, 3/2, 2​

Answer 1

`4x^3-16x^2+19x-6`

Explanation:

P(x)=a(x-r1)(x-r2)(x-r3)

This is a third degree polynomial of leading coefficient a, where r1, r2 and r3 are the roots.

So just replace it with the values you are asked for :

`4\left(x-(3)/(2)\right)\left(x-(1)/(2)\right)\left(x-2\right)\\`

Then expand and you will find the answer :
`4x^3-16x^2+19x-6\\`