the quartic equation x^4+2x^3+14x+15=0 has equal root of 1+2i find the other three root

Question

help me show step plz

Answer 1

since the polynomial has real coefficients, complex roots must come in conjugate pairs. SO, it has another root of 1-2i

(x-(1+2i))(x-(1-2i))
= ((x-1)-2i)((x-1)+2i)
= ((x-1)^2 - (2i)^2)
= x^2-2x+5

Now divide the quartic by that, and you will be left with another quadratic, which you can then work out.

Answer 2

sorry but if i do that is the root going to be in same complex number

Answer 3

I just divided the quadratic that Steve found into the origianl quartic and got
x^2 + 4x + 3
which factors to (x+1)(x+3)

So the other two roots are -1 and -3