Chapter 6: Q. 459 (page 638)

In the following exercises, solve:
$5 a^{2} + 26 a = 24$

Short Answer

Expert verified

On solving, we get $a = \frac{4}{5}, - 6$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$5 a^{2} + 26 a = 24$

Bring all the terms to one side,

$5 a^{2} + 26 a - 24 = 0$

On factoring,

role="math" localid="1644849645692" $5 a^{2} + 30 a - 4 a - 24 = 0 5 a (a + 6) - 4 (a + 6) = 0 (5 a - 4) (a + 6) = 0$

Then,

role="math" localid="1644849654425" $5 a - 4 = 0 a = \frac{4}{5}$

Also,

role="math" localid="1644849661549" $a + 6 = 0 a = - 6$

Step 2. Check the answers.

Substitute $a = \frac{4}{5}$ in the original equation,

$5 {(\frac{4}{5})}^{2} + 26 (\frac{4}{5}) = 24 \frac{16}{5} + \frac{104}{5} = 24 \frac{120}{5} = 24 24 = 24$

This is true.

Substitute $a = - 6$ in the original equation,

$5 {(- 6)}^{2} + 26 (- 6) = 24 180 - 156 = 24 24 = 24$

This is also true.

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In the following exercises, solve:
$5 a^{2} + 26 a = 24$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the answers.

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In the following exercises, solve:5a2+26a=24

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the answers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Geometry

Decision Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve:
$5 a^{2} + 26 a = 24$