SOLUTION: 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

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: 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      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

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(57387) About Me  (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
------------------------
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
---------------------------
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
==============================
Cheers,
Stan H.