Chapter 7: Q. 7.146 (page 884)

Solve:
$b^{2} + 9 b + 14 = 0$

Short Answer

Expert verified

The solutions of the quadratic equations $b^{2} + 9 b + 14 = 0$ are $b = - 7, - 2$

Step by step solution

Step 1. Given Information

An equation:

$b^{2} + 9 b + 14 = 0$

Step 2. Factor the quadratic expression

Factorize the equation,

$b^{2} + 9 b + 14 = 0 (b + 2) (b + 7) = 0$

Step 3. Use the Zero-Product property

Use the Zero Product Property and set each factor to zero.

$b + 2 = 0 b = - 2 b + 7 = 0 b = - 7$

The value of b is $b = - 2, - 7$

Step 4. Check the answer

Check by substituting the values in the original equation,

When $b = - 2$ ,

${(- 2)}^{2} + 9 (- 2) + 14 = 0 4 - 18 + 14 = 0 18 - 18 = 0$

When $b = - 7$ ,

${(- 7)}^{2} + 9 (- 7) + 14 = 0 49 - 63 + 14 = 0 63 - 63 = 0$

Hence the equations hold true.

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Solve:
$b^{2} + 9 b + 14 = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the quadratic expression

Step 3. Use the Zero-Product property

Step 4. Check the answer

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Solve:b2+9b+14=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the quadratic expression

Step 3. Use the Zero-Product property

Step 4. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Applied Mathematics

Decision Maths

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve:
$b^{2} + 9 b + 14 = 0$