SOLUTION: find any rational roots for the equation: 2x^3 - 5x^2 - 11x - 4 =0

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Question 41956: find any rational roots for the equation: 2x^3 - 5x^2 - 11x - 4 =0
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E3+-+5x%5E2+-+11x+-+4+=02x%5E3+%2B+2x%5E2+-+7x%5E2+-+7x+-+4x+-+4+=0
2x%5E2%28x+%2B+1%29+-+7x%28x%2B1%29+-+4%28x%2B1%29+=0
%28x%2B1%29%282x%5E2+-+7x+-+4%29+=0
%28x%2B1%29%282x%5E2+-+8x+%2B+x+-+4%29+=0
%28x%2B1%29%282x%28x+-+4%29+%2B+1%28x+-+4%29%29+=0
%28x%2B1%29%28x-4%29%282x%2B1%29+=+0

Therefore either (x+1) = 0 i.e. x = -1 or (x-4) = 0 i.e. x = 4 or (2x+1) = 0 i.e. x = -1%2F2.
Hence all three roots of the given cubic equation are rational and their values are -1%2F2, -1 and 4.