How do you use the rational root theorem to find the roots of # f(x) = x^3-4x^2-2x+8#?
1 Answer
Use the rational root theorem to identify the possible rational roots to try. Hence find
Explanation:
#f(x) = x^3-4x^2-2x+8#
By the rational root theorem, any rational roots of
So the only possible rational roots are:
#+-1# ,#+-2# ,#+-4# ,#+-8#
#f(2) = 8-16-4+8 = -4#
#f(-2) = -8-16+4+8 = -12#
#f(4) = 64 - 64 - 8 + 8 = 0#
So
#x^3-4x^2-2x+8 = (x-4)(x^2-2)#
The remaining roots are the irrational roots of
#x = +-sqrt(2)#