Chapter 6: Q. 297 (page 627)

In the following exercises, solve:
$(2 x + 1) (x - 3) = - 4 x$

Short Answer

Expert verified

On solving the equation, we get $x = - 1, \frac{3}{2}$ .

Step by step solution

Step 1. Given information.

Consider the given equation,

$(2 x + 1) (x - 3) = - 4 x$

Write the quadratic equation in standard form,

$2 x^{2} - 6 x + x - 3 = - 4 x 2 x^{2} - 9 x - 3 = 0$

Step 2. Factor the quadratic expression.

On factoring, we get,

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

Use the zero product property,

$x + 1 = 0 x = - 1$

Then,

$2 x - 3 = 0 x = \frac{3}{2}$

Step 3. Check the answers.

Substitute $x = - 1$ in the given equation,

$(2 (- 1) + 1) (- 1 - 3) = - 4 (- 1) (- 1) (- 4) = 4 4 = 4$

This is true.

Then,

$(2 (\frac{3}{2}) + 1) (\frac{3}{2} - 3) = - 4 (\frac{3}{2}) (3 + 1) (- \frac{3}{2}) = - 6 - 6 = - 6$

This is also true.

Hence, the answer is $x = - 1, \frac{3}{2}$ .

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In the following exercises, solve:
$(2 x + 1) (x - 3) = - 4 x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor the quadratic expression.

Step 3. Check the answers.

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In the following exercises, solve:2x+1x-3=-4x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor the quadratic expression.

Step 3. Check the answers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve:
$(2 x + 1) (x - 3) = - 4 x$