Monday, May 30, 2011

P(x)=3x^3-10x^2-5x has one root -2/3. What are the other roots?

P(x)=3x^3-10x^2-5x.


The three
roots of this equation can be found by equating  3x^3-10x^2-5x to
0.


=> 3x^3-10x^2-5x
=0


=> x ( 3x^2 - 10x - 5) =
0


So one of the roots is 0


The
other two roots are


x2 = [-b + sqrt (b^2 -
4ac)]/2a


=> x2 = [10 + sqrt (100 +
60)]/6


=> x2 = 10/6 + (sqrt 160) /
6


x3 = [-b - sqrt (b^2 -
4ac)]/2a


=> x3 = [10 - sqrt (100 +
60)]/6


=> x3 = 10/6 - (sqrt 160) /
6


Therefore the roots are 0, 10/6 + (sqrt
160) / 6 and 10/6 - (sqrt 160) / 6.

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