Question

find a polynomial that satisfies the given parameters . A fifth degree polynomial with only two roots

Answer 1

lol did you pick them yet?

Answer 2

2 and 3?

Answer 3

ok fine

Answer 4

then one factor is \((x-2)\) and another has to be \((x-3)\) right?

Answer 5

yes

Answer 6

ok good
now \[(x-2)(x-3)\] is only a polynomial of degree 2 we have to kick it up to degree 5 without introducing any new zeros

Answer 7

any ideas? there are a couple different ways to do it

Answer 8

the conjugates? or imaginary numbers

Answer 9

you could find a quadratic with no real roots like say \(x^2+1\) and multiply it by that, but you would still have a problem since that would only be degree 4 not 5

Answer 10

you can make on zero multiplicity 2, and one zero multiplicity 3, that would do it
do you know what that means (no is a fine answer, just asking)

Answer 11

yes that means both would be x^2

Answer 12

no
the factors would be raised to the power of 2 and 3

Answer 13

for example \[(x-2)^2(x-3)^3\] is a polynomial of degree 5 with two zeros

Answer 14

ohh okay. could it also be (x-2)^3(x-3)^2 ?

Answer 15

@satellite73