Chapter 9: Q.439. (page 983)

Solve by using the quadratic formula.
$4 v^{2} + v - 5 = 0$

Short Answer

Expert verified

The solution is $v = 1$ and $v = - \frac{5}{4}$ .

Step by step solution

Step 1. Given information.

The given equation is $4 v^{2} + v - 5 = 0$ .

Step 2. Write the equation in standard form.

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

$\begin{array}{rcl} 4 v^{2} + v - 5 & = & 0 \\ 4 v^{2} + (1) v + (- 5) & = & 0 \end{array}$

So, here $a = 4, b = 1, c = - 5$ .

Step 3. Apply the quadratic formula.

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

$\begin{array}{rcl} v & = & \frac{- 1 \pm \sqrt{1^{2} - 4 \times 4 \times (- 5)}}{2 (4)} \\ = & \frac{- 1 \pm \sqrt{1 + 80}}{8} \\ = & \frac{- 1 \pm \sqrt{81}}{8} \\ = & \frac{- 1 \pm 9}{8} \end{array}$

Step 4. Solve the equation for v.

$\begin{array}{rcl} v & = & \frac{- 1 + 9}{8} \\ = & \frac{8}{8} \\ = & 1 \end{array}$ and $\begin{array}{rcl} v & = & \frac{- 1 - 9}{8} \\ = & - \frac{10}{8} \\ = & - \frac{5}{4} \end{array}$

Step 5. Simplified answer.

Hence, the required solution is $v = 1$ and $v = - \frac{5}{4}$ .

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Solve by using the quadratic formula.
$4 v^{2} + v - 5 = 0$

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 v.

Step 5. Simplified answer.

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Solve by using the quadratic formula.4v2+v-5=0

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 v.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Solve by using the quadratic formula.
$4 v^{2} + v - 5 = 0$