Question

Given that 3i and -3i are zeros of P(x) = x^4 - 3x^3 + 19x^2 - 27x + 90, find all the other zeros.

Answer 1

HI!!

Answer 2

Hey misty1212!

Answer 3

if \(3i\) is a zero, and \(-3i\) then one of the factors is \[x^2+9\]

Answer 4

Ahhh that makes sense. Thanks!

Answer 5

so \[ x^4 - 3x^3 + 19x^2 - 27x + 90=(x^2+9)(\text{some quadratic})\]

Answer 6

\[\color\magenta\heartsuit\]

Answer 7

:)

Answer 8

So I divided the long polynomial by x^2 + 0x + 9 and got x^2 - 3x + 10. I can't factor that to get any zeros.

Answer 9

That probably means the roots aren't rational. Try the quadratic equation.

Answer 10

@peachpi Ah good idea. Hope I got the right answers. I got (3 +- (i)sqrt(31)) / 2

Answer 11

looks good :)