SOLUTION: Solve the following cubic equations. a) 4x^3+18 = 7x^2+21x b) (x-3)^2 = 4/x

Question 1183632: Solve the following cubic equations.
a) 4x^3+18 = 7x^2+21x
b) (x-3)^2 = 4/x
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
4x^3-7x^2-21x+18=0
Can graph or use synthetic division.
use factor (x-3)
3/ 4== -7==-21==18
===4===5== -6== 0
so (x-3)(4x^2+5x-6)=0
4x^2+5x-6 factors into
x^2+5x-24 or (x-3)(x+8) and then to (4x-3) (x+2)
so x=-2, (3/4), and 3

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b. By inspection, 1 is a root
x(x-3)^2-4=0
x^3-6x^2+9x-4=0
1 is a root
the factors are (x-1)(x^2-5x+4), or (x-1)(x-4)(x-1)
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also can graph each side and look where equal

roots are 1 (repeated), 4

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