SOLUTION: Use the given root to help in writing the given equation as a product of linear and quadratic factors with real coefficients. X^4+3x^3-5x^2-29x-30=0 ; -2-I
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-> SOLUTION: Use the given root to help in writing the given equation as a product of linear and quadratic factors with real coefficients. X^4+3x^3-5x^2-29x-30=0 ; -2-I
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Question 1057226: Use the given root to help in writing the given equation as a product of linear and quadratic factors with real coefficients. X^4+3x^3-5x^2-29x-30=0 ; -2-I Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! If -2-i is one root, then -2+i is another.
That works when a quadratic equation is of the form of x^2+4x+c=0
and x=(1/2)(-4+/-2i)
Therefore, b^2-4ac must be -4, because the sqrt (-4) is +/-2i
b^2-4ac=16-4c=-4
-4c=-20
c=5
x^2+4x+5 is one factor
If this is divided into x^4+3x^3-5x^2-29x-30, using polynomial division, the result is (x^2-x-6), which factors into (x-3)(x+2)
(x^2+4x+5)(x-3)(x+2)
roots are -2+i,-2-i,3,-2
