Question 30145: x^3+3x^2-25x-75=0
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Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! x^3+3x^2-25x-75=0 ----(1)
(x^3+3x^2)-(25x+75)=0 by additive associativity
x^2(x+3)-25(x+3) = 0
x^2p - 25p = 0 where p = (x+3)
p(x^2-25) =0
(x+3)(x^2-25) = 0
(x+3) = 0 implies x = -3
(x^2-25) = 0 gives x^2 = 25
Taking sqrt we get x =+5 or x =-5
Therefore Answer: x = -5,-3 and +5
Verification: x =-5 in x^3+3x^2-25x-75=0 ----(1)
LHS = (-5)^3+3X(-5)^2-25X(-5)-75
=-125+75+125-75
=(125-125)+(75-75)
0+0
=0 =RHS
x =5 in x^3+3x^2-25x-75=0 ----(1)
LHS = (5)^3+3X(5)^2-25X(5)-75
=125+75-125-75
=(125+75)-(125+75)
=0 =RHS
x =-3 in x^3+3x^2-25x-75=0 ----(1)
LHS = (-3)^3+3X(-3)^2-25X(-3)-75
=-27+27+75-75
=0 =RHS
So all the values hold
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