Chapter 9: Q.448. (page 983)

Solve by using the quadratic formula.
$\frac{2}{5} q^{2} + \frac{3}{10} q = \frac{1}{10}$

Short Answer

Expert verified

The solution is $q = \frac{1}{4}$ and $q = - 1$ .

Step by step solution

Step 1. Given information.

The given equation is $\frac{2}{5} q^{2} + \frac{3}{10} q = \frac{1}{10}$ .

Step 2. Write the equation in standard form.

The standard form of the quadratic equation is $a q^{2} + b q + c = 0$ .

The LCM of $(5, 10, 10)$ is $10$ .

So, multiply both sides of the equation by LCM $10$ .

$\begin{array}{rcl} 10 \times \frac{2}{5} q^{2} + 10 \times \frac{3}{10} q & = & \frac{1}{10} \times 10 \\ 4 q^{2} + 3 q & = & 1 \\ 4 q^{2} + 3 q + (- 1) & = & 0 \end{array}$

So, here $a = 4, b = 3, c = - 1$ .

Step 3. Apply the quadratic formula.

The quadratic formula is $q = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

$\begin{array}{rcl} q & = & \frac{- 3 \pm \sqrt{3^{2} - 4 \times 4 \times (- 1)}}{2 \times 4} \dots \dots (a = 4, b = 3, c = - 1) \\ = & \frac{- 3 \pm \sqrt{9 + 16}}{8} \\ = & \frac{- 3 \pm \sqrt{25}}{8} \\ = & \frac{- 3 \pm 5}{8} \end{array}$

Step 4. Solve the equation for q.

$\begin{array}{rcl} q & = & \frac{- 3 + 5}{8} \\ = & \frac{2}{8} \\ = & \frac{1}{4} \end{array}$ and $\begin{array}{rcl} q & = & \frac{- 3 - 5}{8} \\ = & \frac{- 8}{8} \\ = & - 1 \end{array}$

Step 5. Simplified answer.

Hence, the required solution is $q = \frac{1}{4}$ and $q = - 1$ .

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Solve by using the quadratic formula.
$\frac{2}{5} q^{2} + \frac{3}{10} q = \frac{1}{10}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in standard form.

Step 3. Apply the quadratic formula.

Step 4. Solve the equation for q.

Step 5. Simplified answer.

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Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in standard form.

Step 3. Apply the quadratic formula.

Step 4. Solve the equation for q.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Solve by using the quadratic formula.
$\frac{2}{5} q^{2} + \frac{3}{10} q = \frac{1}{10}$