SOLUTION: Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) P(x)=2x^3+15x^2+24x-16

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) P(x)=2x^3+15x^2+24x-16      Log On


   

Question 1086383: Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x)=2x^3+15x^2+24x-16
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=2x%5E3%2B15x%5E2%2B24x-16+
P%28x%29=+2x%5E3+-+x%5E2%2B+16x%5E2-+8x%2B32x-16
P%28x%29=+%282x%5E3+-+x%5E2%29%2B+%2816x%5E2-+8x%29%2B%2832x-16%29
P%28x%29=x%5E2+%282x+-+1%29%2B8x+%282x-+1%29%2B16%282x-1%29
P%28x%29=%28x%5E2+%2B+8x%2B16%29+%282x+-+1%29
P%28x%29=%28x+%2B+4%29%5E2+%282x+-+1%29
solutions:
0=%28x+%2B+4%29%5E2=>x=-4
0=+%282x+-+1%29=>2x=1=>x=1%2F2
zeros are:-4,1%2F2

+graph%28+600%2C+600%2C+-10%2C+10%2C+-20%2C+10%2C%28x+%2B+4%29%5E2%2A%282x+-+1%29%29+

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x)=2x^3+15x^2+24x-16
Graph to find zero at -4
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Use synthetic division::
-4....2....15....24....-16
......2....7.....-4...|..0
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Use quadratic equation::
x = [-7+-sqrt(49-4*2*-4)]/4
x = [-7+- sqrt(81)]/4
x = (-7+9)/4 or x = (-7-9)/4
x = -4 or x = 1/2
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Ans: x = -4,-4,1/2
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Cheers,
Stan H.
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