SOLUTION: Use the given zero to find all other zeros. Zero:2i Equation: F(x)=2x^3+3x^2+8x+12 Thanks in advance!

Question 1178287: Use the given zero to find all other zeros.
Zero:2i
Equation: F(x)=2x^3+3x^2+8x+12
Thanks in advance!
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Quadratic factor of F is . Use this to help find your other two zeros. Try polynomial division or whatever other method you find helpful.

.

2x 3 ______________________________ x^2+0x+4 | 2x^3 +3x^2 + 8x + 12 | 2x^3 + 0x^2 + 8x | ----------------- 0 3x^2 0x 12 3x^2 0x 12 ---------------- 0 0 0

The zero found here, for .

Or this could work too:

----------and the other zero is .
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Use the given zero to find all other zeros.
Zero: =>so, you also have
using root product rule we have

equal given quation to zero and factor it: note one factor should be

=>third root is:
=>=>

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Use the given zero to find all other zeros.
Zero:2i
Equation: F(x)=2x^3+3x^2+8x+12
Thanks in advance!

.
It's NOT as complex as the other 2 people state.
You don't even need to use the 2 roots that're given (2i and its conjugate, - 2i) because when EACH binomial, from left to right, is factored, we get:
You MIGHT be able to recognize as the EXPANDED form of the given zero, 2i and its conjugate.
With that being said, the other factor, as seen above, is 2x + 3, which gives us: 2x + 3 = 0 ====> 2x = - 3, and ultimately, the other zero, or:
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