SOLUTION: Find the range of values for which the equation x^3-qx+q+3=0 has real roots

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Question 1129569: Find the range of values for which the equation x^3-qx+q+3=0 has real roots
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3-qx%2Bq%2B3=0+
x%5E3-q%28x-1-3%29=0+

x%5E3=q%28x-4%29+
q=x%5E3%2F%28x-4%29+ ->x%3C%3E4; => to have real roots, x must be greater than 4
the range of values:
(4,infinity)


check few of them:
x=4.1
q=4.1%5E3%2F%284.1-4%29=689.21=>x%5E3-689.21x%2B689.21%2B3=0=>x%5E3-689.21x-692.21=0

+graph%28+600%2C+600%2C+-50%2C+50%2C+-5000%2C+5000%2Cx%5E3-689.21x-692.21%29+
x=5
q=5%5E3%2F%285-4%29=75=>x%5E3-75x%2B75%2B3=0=>x%5E3-75x-73=0
+graph%28+600%2C+600%2C+-30%2C+30%2C+-300%2C+300%2Cx%5E3-75x-73%29+

x=5
q=6%5E3%2F%286-4%29=108=>x%5E3-108x%2B108%2B3=0=>x%5E3-108x-111=0
+graph%28+600%2C+600%2C+-30%2C+30%2C+-300%2C+300%2Cx%5E3-108x-111%29+