SOLUTION: 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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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       Log On


   

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

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
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
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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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A4%2A9+%29%29%2F%282%2A4%29+
x+=+%284+%2B-+sqrt%28+16-144%29%29%2F%288%29+
x+=+%284%2B-+sqrt%28-128%29%29%2F%288%29+
x+=+%284%2B-8sqrt%28-2%29%29%2F%288%29+
x+=+%284%2F8%29%2B-sqrt%28-2%29%29
x=%281%2F2%29%2Bi%2Asqrt%282%29...and..
..x=%281%2F2%29-i%2Asqrt%282%29...