Chapter 11: Q. 430 (page 1069)

In the following exercises, solve.
$q^{3} + 3 q^{2} + 2 q = 0$

Short Answer

Expert verified

Answer is $q = 0, q = - 1, q = - 2$

Step by step solution

Step 1. Given

The equation is $q^{3} + 3 q^{2} + 2 q = 0$

Step 2. Simplify the equation

$q^{3} + 3 q^{2} + 2 q = 0 q (q^{2} + 3 q + 2) = 0 q (q^{2} + 2 q + q + 2) = 0 q (q (q + 2) + 1 (q + 2)) = 0 q (q + 2) (q + 1) = 0$

So,

$q = 0$

and

$q + 2 = 0 q = - 2$

and

$q + 1 = 0 q = - 1$

Step 3. Check all the values

Put $q = 0$ in the original equation,

$q^{3} + 3 q^{2} + 2 q = 0 0^{3} + 3 {(0)}^{2} + 2 (0) = 0 0 = 0$

True

Now put $q = - 2$ in original equation,

$q^{3} + 3 q^{2} + 2 q = 0 {(- 2)}^{3} + 3 {(- 2)}^{2} + 2 (- 2) = 0 - 8 + 12 - 4 = 0 0 = 0$

True

Now put $q = - 1$ in the original equation,

$q^{3} + 3 q^{2} + 2 q = 0 {(- 1)}^{3} + 3 {(- 1)}^{2} + 2 (- 1) = 0 - 1 + 3 - 2 = 0 0 = 0$

True

Step 4. Required answer

Answer is $q = 0, q = - 2, q = - 1$

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In the following exercises, solve.
$q^{3} + 3 q^{2} + 2 q = 0$

Short Answer

Step by step solution

Step 1. Given

Step 2. Simplify the equation

Step 3. Check all the values

Step 4. Required answer

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In the following exercises, solve. q3+3q2+2q=0

Short Answer

Step by step solution

Step 1. Given

Step 2. Simplify the equation

Step 3. Check all the values

Step 4. Required answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$q^{3} + 3 q^{2} + 2 q = 0$