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

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


   

Question 1183632: Solve the following cubic equations.
a) 4x^3+18 = 7x^2+21x
b) (x-3)^2 = 4/x
Answer by Boreal(15235) About Me  (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
graph%28300%2C300%2C-5%2C5%2C-25%2C25%2C4x%5E3-7x%5E2-21x%2B18%29
-
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)
-
also can graph each side and look where equal
graph%28300%2C300%2C-5%2C5%2C-10%2C10%28x-3%29%5E2%2C%284%2Fx%29%29
roots are 1 (repeated), 4
graph%28300%2C300%2C-5%2C5%2C-10%2C10%2C%28x-3%29%5E2%2C%284%2Fx%29%29