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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Non-linear equations in one variable

Grade: 1300-a Lesson: S1-L6

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Solve the nonlinear equation \$11x^3 +12 x^2 + x = 0\$.
2	Step	Rewrite the equation into quadratic form	\$ x(11x^2 + 12x + 1) = 0 \$ x = 0, \$ 11x^2 + 12x + 1 = 0 \$
3	Formula:	The quadratic formulae	\$ x = (- b ± \sqrt(b^2 - 4ac)) / (2a) \$
4	Step	Plug in the corresponding values using the quadratic formulae	a = 11, b = 12, and c = 1 \$ x = (-12 ± \sqrt(12^2 - 4 times11 times1)) / (2 times11) \$ \$ x = (-12 ± 10) / (22) \$
5	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\$
6	Step	Therefore, the solutions to the non-linear equation \$11x^3 + 12x^2 + x = 0\$ are \$ x = - 1/11 and x = - 1\$.
7	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	\$ x = 1/11 and x = -1\$
8	Choice.B	This is the correct option. Substituting \$x = −1/11\$ and x = -1 into the equation yields zero, which satisfies the equation	\$ x = -1/11 and x = -1\$
9	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	\$ x = -2/11 and x = 11\$
10	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	x = 1 and x = 3
11	Answer	Option	B
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

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

Step

Rewrite the equation into quadratic form

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

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

Formula:

The quadratic formulae

\$ x = (- b ± \sqrt(b^2 - 4ac)) / (2a) \$

Step

Plug in the corresponding values using the quadratic formulae

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

\$ x = (-12 ± \sqrt(12^2 - 4 times11 times1)) / (2 times11) \$

\$ x = (-12 ± 10) / (22) \$

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\$

Step

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

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

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

Choice.B

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

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

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

\$ x = -2/11 and x = 11\$

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

x = 1 and x = 3

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?