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Question 46217: Can someone please help me with the following: What are all the possible rational roots (using synthetic division to find an actual root, then using this root to solve the equation) for x^3 + 5x^2 + 12x - 18 = 0 ?!?!?
Can you please explain the steps involved as well as the solution (as I am fairly lost)?
THANK YOU!!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Can someone please help me with the following: What are all the possible rational roots (using synthetic division to find an actual root, then using this root to solve the equation) for x^3 + 5x^2 + 12x - 18 = 0 ?!?!?
TRY FACTORS OF CONSTANT=-18....PLUS OR MINUS 1,2,3,6,9,18 FOR X ..
HERE X=1 GIVES
1+5+12-18-0...OK...SO X=1 IS A ROOT SO X-1 IS A FACTOR.NOW DIVIDE
1|...1......5......12........-18
.....0......1.......6.........18
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.....1......6.......18.........0
X^2+6X+18 IS QUOTIENT..NOW FACTORISE OR USE QUADRATIC FORMULA.
HERE B^2-4AC= 36-4*18*1=-VE...SO NO ROOTS
HENCE THERE IS ONLY 1 REAL ROOT = X=1
Can you please explain the steps involved as well as the solution (as I am fairly lost)?
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