How do you find all the zeros of #x^3-7x-6#?

Question

3506 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-23T14:19:26

#x^3-7x-6=(x+1)(x+2)(x-3)#

Given a polynomial in which the maximum power therm coefficient is 1, the constant therm is the product of its roots.

Examining the polynomial

#p_3(x) = x^3-7x-6#

we can conclude that #6 = x_1*x_2*x_3#
such that #p_3(x) = (x-x_1)(x-x_2)(x-x_3)#.

Supposing that the roots are integers we can try the set of values

#{pm 1, pm 2, pm 3}# which are potential #-6# factors

Easily we can verify that

#p_3(-1) = p_3(-2) = p_3(3) = 0# so we found the three roots and we can state:

#x^3-7x-6=(x+1)(x+2)(x-3)#