SOLUTION: Use synthetic division to determine which pair of integers provide both a lower and an upper bound for the zeros of {{{f(X)=2X^4-X^3-23X^2+46X-24}}}
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-> SOLUTION: Use synthetic division to determine which pair of integers provide both a lower and an upper bound for the zeros of {{{f(X)=2X^4-X^3-23X^2+46X-24}}}
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Question 550005: Use synthetic division to determine which pair of integers provide both a lower and an upper bound for the zeros of Found 2 solutions by stanbon, lwsshak3:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! f(X)=2X^4-X^3-23X^2+46X-24
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The coefficients add up to zero, so x = 1 is a root:
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Use synthetic division to help find the 2 remaining roots:
1)...2....-1....-23.....46.....-24
......2.....1.....-22....24....|..0
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Quotient: 2x^3+x^2-22x+24
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I graphed the cubic and found a zero at x = 3/2
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(3/2))....2....1....-22....24
...........2....4.....-16...|0
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Quotient: 2x^2+4x-16
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Factor:
= 2(x^2+2x-8)
= 2(x+4)(x-2)
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The roots are 1, 3/2 , 2 , -4
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Cheers,
Stan H.
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You can put this solution on YOUR website! f(X)=2X^4-X^3-23X^2+46X-24
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Using the Rational Roots Theorem:
....0....|......2......-1......-23.......46.......-24
....1....|......2.......1.......-22.......24..........0 (1 is a root)
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....0....|......2.......1.......-22.......24
....2....|......2.......5.......-12.......0 (2 is a root)
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....0....|......2.......5.......-12
....3....|......2......11........21 (3 is upper bound-all numbers positive)
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....0....|......2........5......-12
..-1....|......2........3......-15
..-2....|......2........1......-14
..-3....|......2......-1......-9
..-4....|......2......-3.......0 (-4 is a root)
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....0....|......2......-3
..-5....|......2......-13 (-5 is lower bound-alternate sign of numbers)
f(x)=(x-1)(x-2)(x+4)(2x-3)
ans:
Upper bound and lower bound for zeros: x=3 and x=-5 respectivelly
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