Chapter 9: Q.441. (page 983)

Solve by using the quadratic formula.
$3 m^{2} + 8 m + 2 = 0$

Short Answer

Expert verified

The solution is $m = \frac{- 4 \pm \sqrt{10}}{3}$ .

Step by step solution

Step 1. Given information.

The given equation is $3 m^{2} + 8 m + 2 = 0$ .

Step 2. Write the equation in standard form.

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

$3 m^{2} + 8 m + 2 = 0$

So, here $a = 3, b = 8, c = 2$ .

Step 3. Apply the quadratic formula.

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

Substitute $a = 3, b = 8, c = 2$ in the above result.

$\begin{array}{rcl} m & = & \frac{- 8 \pm \sqrt{8^{2} - 4 \times 3 \times 2}}{2 \times 3} \\ = & \frac{- 8 \pm \sqrt{64 - 24}}{6} \\ = & \frac{- 8 \pm \sqrt{40}}{6} \\ = & \frac{- 8 \pm 2 \sqrt{10}}{6} \\ = & \frac{2 (- 4 \pm \sqrt{10})}{2 \times 3} \\ = & \frac{- 4 \pm \sqrt{10}}{3} \end{array}$

Step 4. Simplified answer.

Hence, the required solution is $m = \frac{- 4 \pm \sqrt{10}}{3}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve by using the quadratic formula.
$3 m^{2} + 8 m + 2 = 0$

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. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Mechanics Maths

Logic and Functions

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve by using the quadratic formula.3m2+8m+2=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. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Mechanics Maths

Logic and Functions

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve by using the quadratic formula.
$3 m^{2} + 8 m + 2 = 0$