Question 550005
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