Question 18077
p(x)=4x^3-16x^2+21x-27 has three real roots one of them is 3 and a conjugate complex pair of roots which is _____ +- _____i 
************************
the wording of the problem is not correct ...to say the eqn. has 3 real roots
and then ask for conjugate complex pair of roots which is _____ +- _____i 
ANY WAY LET US SOLVE AND SEE...

since 3 is a root x-3 is a factor.let us divide with x-3 using short division.
3..|..4....-16....21....-27
...|..0.....12....-12....27
----------------------------------------------- 
......4....-4.....9......0 is remainder
 4x^2-4x+9=0...using the formula for roots of ax^2+bx+c=0 ,we have...
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-(-4) +- sqrt( (-4)^2-4*4*9 ))/(2*4) }}} 
{{{x = (4 +- sqrt( 16-144))/(8) }}} 
{{{x = (4+- sqrt(-128))/(8) }}}
 {{{x = (4+-8sqrt(-2))/(8) }}}
{{{x = (4/8)+-sqrt(-2))}}}
{{{x=(1/2)+i*sqrt(2)}}}...and..
..{{{x=(1/2)-i*sqrt(2)}}}...