If then another root is .
Now divide the polynomial by .
I need a little help with this please:
Use the given zero to find the remaining zeros of the polynomial:
h(x) = x^4 - 9x^3 + 21x^2 +21x -130; zero: 3-2i
Now i kno all about the zeros when complex existing with their conjugates, i know all about factoring using the different rules and theorems. Had this been a real root, i would've had to divide using long division and testing for roots to factor further, but with this complex one, i am not sure how to do this. Can long division be done on a complex root??? I am not seeing the way of this one. I did one before that had a zero of -2i, but now that the 3 is there i am not sure what to do. Can i get some help please????
Thanks a lot.
ok this i know... but how do i do this division, now? and also, how do you get those well laid out math symbols on this or on the pc on the whole? can you give me a little help on that division? i think i only know how to divide by a simple divisor, one of degree 1 (eg x+1)...
You can do synthetic division by complex roots. It's a little tricky, but it can be done.
First, divide by 3 - 2i. We know that the remainder will be zero:
Now, let's divide the quotient by 3 + 2i, the conjugate of 3 - 2i:Code:3 - 2i| 1 -9 21 21 -130 ------- 3-2i -22+6i 9+20i 130 -------------------------------- 1 -6-2i -1+6i 30+20i 0
So you're left with the quadraticCode:3 + 2i| 1 -6-2i -1+6i 30+20i ------- 3+2i -9-6i -30-20i --------------------------- 1 -3 -10 0
which factors into
The two remaining roots are -2 and 5.
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For long division see this: Polynomial Long Division
To write mathematical symbols see Latex Tutorial in Latex help section on this forum.