Chapter 2: Q. 4 (page 126)

Find the real solutions of the equation:
$6 x^{2} - 5 x + 1 = 0$

Short Answer

Expert verified

The solution of the given equation is:

$x = \frac{1}{2} x = \frac{1}{3}$

Step by step solution

Step 1. Given information

The given equation is $6 x^{2} - 5 x + 1 = 0$

Step 2. Factorise the equation

Using the factorisation method, we get:

$6 x^{2} - 5 x + 1 = 0 6 x^{2} - 3 x - 2 x + 1 = 0 3 x (2 x - 1) - (2 x - 1) = 0 [t a k i n g o u t 3 x a n d - 1 a s c o m m o n] (2 x - 1) (3 x - 1) = 0$

Step 3. Evaluating the value

Using zero product property, we get:

$(2 x - 1) = 0 2 x = 1 x = \frac{1}{2}$

$3 x - 1 = 0 3 x = 1 x = \frac{1}{3}$

Step 4. Verify the solution

Substituting $x = \frac{1}{2}$ in the given equation, we get:

$6 x^{2} - 5 x + 1 = 0 6 {(\frac{1}{2})}^{2} - 5 (\frac{1}{2}) + 1 = 0 6 \times \frac{1}{4} - 5 \times \frac{1}{2} + 1 = 0 \frac{3}{2} - \frac{5}{2} + 1 = 0 \frac{- 2}{2} + 1 = 0 - 1 + 1 = 0 0 = 0$

This is true.

Substituting role="math" localid="1645888581245" $x = \frac{1}{3}$ in the given equation, we get:

$6 x^{2} - 5 x + 1 = 0 6 {(\frac{1}{3})}^{2} - 5 (\frac{1}{3}) + 1 = 0 6 \times \frac{1}{9} - 5 \times \frac{1}{3} + 1 = 0 \frac{2}{3} - \frac{5}{3} + 1 = 0 \frac{2 - 5}{3} + 1 = 0 \frac{- 3}{3} + 1 = 0 - 1 + 1 = 0 0 = 0$

This is true.

Thus the solution of the given function is:

role="math" localid="1645888988809"

x = \frac{1}{2} x = \frac{1}{3}

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Find the real solutions of the equation:
$6 x^{2} - 5 x + 1 = 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factorise the equation

Step 3. Evaluating the value

Step 4. Verify the solution

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Find the real solutions of the equation:6x2-5x+1=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factorise the equation

Step 3. Evaluating the value

Step 4. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the real solutions of the equation:
$6 x^{2} - 5 x + 1 = 0$