Factor the polynomial and use the factored form to find the zeros. P(x) = x^4 − 3x^3 + 2x^2

Question

So, I thought the zeros would be 0,1,2. But, the answers were wrong, I do not know what else it would be. Thank you

Answer 1

P(x) = x⁴ − 3x³ + 2x²

P(x) = x²(x² - 3x + 2)

P(x) = x·x(x-1)(x-2)

 

Zeros are at x = 0, 0, 1, 2

 

P(x) is degree 4, so it will have four roots.  You only entered three which is probably why it came up as wrong.  The x² term has a multiplicity of 2, so it counts twice.