1

Problem

Solve the nonlinear equation \$11x^3 +12 x^2 + x = 0\$.

2

Step

The given nonlinear equation is

\$11x^3 + 12 x^2 + x = 0\$

3

Step

Rewrite the equation into quadratic form:

\$ x(11x^2 + 12x + 1) = 0 \$

\$x = 0, 11x^2 + 12x + 1 = 0 \$

4

Formula

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

5

Step

Plug in the corresponding values using the quadratic formula:

a = 11, b = 12, and c = 1

\$ x = (-12 ± \sqrt((12)^2 - 4 \times 11 \times1)) / (2 \times 11) \$

\$ x = (-12 ± 10) / (22) \$

6

Step

Make it simplified and here we have two possible solutions are:

\$ x = (-12 + 10) / (22) and x = (-12 - 10) / (22)\$

\$ x = (-\cancel(2)^1) / (\cancel(22)^11) and x = (\cancel(-22)^1) / (\cancel(22)^1)\$

\$ x = - 1/(11) and x = -1\$

7

Solution

Therefore, the solutions to the non-linear equation \$11x^3 + 12x^2 + x = 0\$ are \$ x = - 1/(11) and x = - 1\$.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This is incorrect. Substituting \$x = 1/(11)\$​ into the equation results in a nonzero value, thus not satisfying the equation. Also, x = - 1 doesn’t satisfy the equation either

Wrong \$ x = 1/(11) and x = -1\$

10

Choice-B

This is the correct option. Substituting \$x = −1/(11)\$​ and x = -1 into the equation yields zero, which satisfies the equation

Correct \$ x = -1/(11) and x = -1\$

11

Choice-C

This is incorrect. Substituting \$x = - 2/(11)\$​ into the equation results in a nonzero value, thus not satisfying the equation. Also, x = 11 doesn’t satisfy the equation either

Wrong \$ x = -2/(11) and x = 11\$

12

Choice-D

This is incorrect. Substituting x = 1 into the equation results in a nonzero value, thus not satisfying the equation. Also, x = - 3 doesn’t satisfy the equation either

Wrong x = 1 and x = 3

13

Answer

Option

B

14

Sumup

Please summarize choices