SOLUTION: Find all the real zeros of function f(x)=12x^4+35x^3+144x^2+114x+20 I already have x= -2/3

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Question 63055: Find all the real zeros of function f(x)=12x^4+35x^3+144x^2+114x+20
I already have x= -2/3
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all the real zeros of function f(x)=12x^4+35x^3+144x^2+114x+20
I already have x= -2/3
Also x=-1/4 is a zero
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Therefore (4x+1)(3x+2) =12x^2+11x+2 divides f(x)
Using long division you can find the remaining quotient, which is:
Quotient: x^2+2x+10
Use the quadratic formula to find the last two zeroes:
x=[-2+-sqrt(4-4(10)]/2
x=[-2+-6i]/2
x=-1+3i or x=-1-3i
These are the missing zeroes.
Cheers,
Stan H.