Question 125340: Sketch the following polynomial and identify all intercepts, zeros, and include a chart showing points that are necessary to sketch the polynomial:
y=3x^3-14x^2+17x-6
Thanks in advance for the help. I already know how to make the chart, but the rest of the problem is troubling me.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sketch the following polynomial and identify all intercepts, zeros, and include a chart showing points that are necessary to sketch the polynomial:
y=3x^3-14x^2+17x-6
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the coefficients add up to zero so x=1 is a zero of the polynomial.
Use synthetic division to find the other factor:
1)....3....-14....+17....-6
........3.....-11....6...|..0
Quotient: 3x^2-11x+6
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Use the quadratic formula to find the remaining zeroes:
x = [11 +- sqrt(121-4*3*6]/6
x = [11 +- sqrt(49)]/6
x = 3 or x = 2/3 or x = 1
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Cheers,
Stan H.
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