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

Question

asked May 16, 2023 163k views

1 Answer

Alina Li · Answer 1 · 2023-05-21T01:02:34+0000

Answer:

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 :
$4x^3-16x^2+19x-6\\$