Chapter 4: Q. 31 (page 163)

In Exercises 28-33 $x$ represents the length of a segment. When a value of $x$ doesn't make sense as a length, eliminate that value of $x$ .
$2 x^{2} + x - 3 = 0$

Short Answer

Expert verified

The length of the segment is $x = 1$ .

Step by step solution

- Understand the concept used

If $a x^{2} + b x + c = 0$ , with $a \neq 0$ , then $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ . Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values

It is given that $2 x^{2} + x - 3 = 0$ .Using quadratic formula $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 2 for a, 1 for b and -3 for c.

Put the values in the formula and get $x = \frac{- (1) \pm \sqrt{{(1)}^{2} - 4 \times (2) \times (- 3)}}{2 (2)}$ .

- Simplify for x

Simplify the expression for x.

$\begin{matrix} x = \frac{- (1) \pm \sqrt{{(1)}^{2} - 4 \times (2) \times (- 3)}}{2 (2)} \\ = \frac{- 1 \pm \sqrt{1 + 24}}{4} \\ = \frac{- 1 \pm \sqrt{25}}{4} \\ = \frac{- 1 \pm 5}{4} \end{matrix}$

Therefore, either $x = \frac{- 1 + 5}{4} = \frac{4}{4}$ or $x = \frac{- 1 - 5}{4} = \frac{- 6}{4}$ that is., either $x = 1$ or $x = - \frac{3}{2}$ . Here, the $x$ is having two values 1 and $- \frac{3}{2}$ . Since $x$ , is a length of a segment that could not be negative or zero, therefore, the value of $x$ is 1.

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In Exercises 28-33 $x$ represents the length of a segment. When a value of $x$ doesn't make sense as a length, eliminate that value of $x$ .
$2 x^{2} + x - 3 = 0$

Short Answer

Step by step solution

- Understand the concept used

- Substitute the values

- Simplify for x

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In Exercises 28-33 xrepresents the length of a segment. When a value of xdoesn't make sense as a length, eliminate that value ofx.2x2+x−3=0

Short Answer

Step by step solution

- Understand the concept used

- Substitute the values

- Simplify for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Applied Mathematics

Pure Maths

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Exercises 28-33 $x$ represents the length of a segment. When a value of $x$ doesn't make sense as a length, eliminate that value of $x$ .
$2 x^{2} + x - 3 = 0$