SOLUTION: Hi there, Could one of the tutors help me with this homework question? Solve for x: 2x^3 + 6x^2 - x = 3.(4 marks)

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Question 190676: Hi there, Could one of the tutors help me with this homework question?
Solve for x: 2x^3 + 6x^2 - x = 3.(4 marks)
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
We need to factor it first.
2x%5E3+%2B+6x%5E2+-+x+=+3
2x%5E3+%2B+6x%5E2+-+x-3+=+0
%282x%5E3+%2B+6x%5E2%29+-+%28x%2B3+%29=+0 grouping the terms
2x%5E2%28x%2B3%29+-+%28x%2B3+%29=+0 Factor 2x%5E3+%2B+6x%5E2 into 2x%5E2%28x%2B3%29
%28x%2B3%29%282x%5E2-+1%29=+0
As %28x%2B3%29%282x%5E2-+1%29=+0, then either x%2B3=0 or 2x%5E2-+1=0
Solving x%2B3=0, we have x=-3
Solving 2x%5E2-+1=0, we have
2x%5E2=1
x%5E2=1%2F2
x=1%2Fsqrt%282%29 or x=-1%2Fsqrt%282%29
So the three roots are:
x=-3
x=1%2Fsqrt%282%29
x=-1%2Fsqrt%282%29
Normally, the last two roots need to be rationalized. So the final result is:
x=-3
x=sqrt%282%29%2F2
x=-sqrt%282%29%2F2