SOLUTION: this is for college algebra: verify that 3i is a zero of p(x) = x^3- 5x^2 + 9x - 45 and then proceed to use the conjugate pair theorem to find the remaining zeros
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-> SOLUTION: this is for college algebra: verify that 3i is a zero of p(x) = x^3- 5x^2 + 9x - 45 and then proceed to use the conjugate pair theorem to find the remaining zeros
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Question 62289: this is for college algebra: verify that 3i is a zero of p(x) = x^3- 5x^2 + 9x - 45 and then proceed to use the conjugate pair theorem to find the remaining zeros Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! verify that 3i is a zero of p(x) = x^3- 5x^2 + 9x - 45
I'll let you do the hard part.
Find p(3i)
If you get an answer of zero, 3i is a zero.
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and then proceed to use the conjugate pair theorem to find the remaining zeros
Assuming you did get a zero for p(3i), -3i is also a zero.
So the cubic is divisible by (x-3i)(x+3i)=x^2+9
Divide p(x) by x^2+9 to find the remaining factor
which is x-5.
So the remaining zero is x=5.
Cheers,
Stan H.
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