1

Problem

Solve the non-linear equation \$x^3 - 5x^2 + 6x = 0\$.

2

Step

The given non-linear equation

\$x^3 - 5x^2 + 6x = 0\$

3

Step

Rewrite the equation into quadratic form:

\$x(x^2 - 5x + 6) = 0\$

x = 0 and \$x^2 - 5x + 6 = 0\$

4

Formula

The quadratic formulae is \$ x = (- b ± \sqrt(b^2 - 4ac)) / (2a) \$.

5

Step

Plug in the corresponding values using the quadratic formulae:

Where a = 1, b = - 5, and c = 6

\$x = (-(- 5) ± \sqrt((-5)^2 - 4(1)(6))) / (2(1))\$

\$x = (5 ± \sqrt(1)) / 2\$

6

Step

The two possible answers are:

\$x = (5 + 1) / 2 \$ or \$x = (5 - 1) / 2\$

x = 3 or x = 2

7

Solution

Therefore, the solutions to the equation is \$x^3 - 5x^2 + 6x = 0 are x = 0, x = 2, and x = 3\$.

8

Sumup

Please summarize steps

Choices

9

Choice-A

x = - 2 and x = - 3, does not satisfy the equation when substituted back into \$x^3 - 5x^2 + 6x = 0\$, so it is not correct

Wrong x = - 2 and x = - 3

10

Choice-B

It is not correct because it provides the values x = 2 and x = 3, but it misses the solution x = 0

Wrong x = 2 and x = 3

11

Choice-C

Option C, x = 1 and x = - 2, is incorrect because x = 1 is not a solution to the equation

Wrong x = 1 and x = - 2

12

Choice-D

This is correct as it includes all the accurate roots of the provided equation

Correct x = 0, x = 2, and x = 3

13

Answer

Option

D

14

Sumup

Please summarize choices