.
#1 Factor the expression on the left side of the equation. Then solve the equation.
x^3 - 2x^2 - 5x = 0
A. 0, -1 +/- sqrt 24
B. -5, 0, 3
C. 0, 1 +/- sqrt 6
D. 0, -1 +/- sqrt 6
~~~~~~~~~~~~~~~~~~~~~
Factor:
= .
Solve the equation = . Apply the quadratic formula
= = = = .
The roots of the original equation are 0, and .
The answer is option C.
#2 Factor the expression on the left side of the equation. Then solve the equation.
x6 + 128x3 + 4096 = 0
A. 4, 2 +/- 2i*sqrt 3
B. 4 multiplicity of 2, 2 +/- 2i*sqrt3 multiplicity of 2
C. -4, 2 +/- 2i*sqrt 3
D. - 4 multiplicity of 2, 2 +/- 2i*sqrt3 multiplicity of 2
Factor
= . (1)
Now solve
= . (2)
It is reduced to
= , (3)
= ,
= , , , or, which is the same
, , , or, which is the same again
, . (4).
Thus the solution of (3) are the roots (4).
Hence, the solution of (1) are the roots listed under the option D)