How do you solve y^3 - y^2 +4y -4 = 0?

1 Answer
Feb 21, 2016

Solution of the equation is y=1, 2i or -2i.

Explanation:

In the equation y^3−y^2+4y−4=0, factors of constant term -4 are, (1,-1,2,-2,4,-4). So, first identify which among these satisfies the equation. As is apparent y=1 satisfies the equation and hence (y-1) is one such factor.

As such factorizing y^3−y^2+4y−4=0 , we get

y^2*(y-1)+4(y-1)=0

or (y^2+4)(y-1)=0, i.e. either y=1 or y^2+4=0.

AS the latter cannot be factorized, we get its roots by using general form of quadratic equation ax^2+bx+c=0 which are (-b+-sqrt(b^2-4ac))/(2a).

As a=1, b=0, c=4 roots of y^2+4=0 are (0+-sqrt(0-4*4*1))/(2a) or +-sqrt(-16)/2 or +-(4i)/2 i.e. +-2i

Hence solution of the equation is y=1, 2i or -2i.