Question

3x^4+5x^3+25x^2+45x-18 zeros:3i,-3i. I need help finding the other two zeros

Answer 1

if those are the two zeros, then one factor is \((x+3i)(x+3i)=x^2+9\)

Answer 2

Yeah I got that part

Answer 3

that means
\[3x^4+5x^3+25x^2+45x-18 =(x^2+9)(\text{something})\]
find the something by either thinking or by division

Answer 4

i like the think method, it is easier than dividing

Answer 5

for example, the first term has to be \(3x^2\) otherwise you are not going to get \(3x^4\) when you multiply

Answer 6

the last term has to be \(-2\) so you will get \(-18\) when you multiply

Answer 7

\[3x^4+5x^3+25x^2+45x-18 =(x^2+9)(3x^2+bx-2)\] and all you need is \(b\)

Answer 8

Is the b 5x?

Answer 9

yes

Answer 10

\[3x^2+5x-2\] is the other factor, which in turn factors as \[(3x-1)(x+2)\]

Answer 11

OMG thank you

Answer 12

yw