Question

Find the roots of the following equation

Answer 1

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Answer 2

Answer:

The roots of the quadratic equation are

x = ( 3 + √13 ) / 2 and x = ( 3 - √13 ) / 2.

Step-by-step-explanation:

The given quadratic equation is

2x - ( 2 / x ) = 6.

We have to find the roots of the quadratic equation.

Now,

2x - ( 2 / x ) = 6

⇒ ( 2x² - 2 ) / x = 6

⇒ 2x² - 2 = 6x

⇒ 2x² - 2 - 6x = 0

⇒ 2x² - 6x - 2 = 0

⇒ 2 ( x² - 3x - 1 ) = 0

⇒ x² - 3x - 1 = 0

Comparing with ax² + bx + c = 0, we get,

• a = 1
• b = - 3
• c = - 1

Now,

b² - 4ac = ( - 3 )² - 4 * 1 * ( - 1 )

⇒ b² - 4ac = 9 + 4

⇒ b² - 4ac = 13

Now, by quadratic formula,

x = [ - b ± √( b² - 4ac ) ] / 2a

⇒ x = [ - ( - 3 ) ± √13 ] / ( 2 * 1 )

⇒ x = ( 3 ± √13 ) / 2

⇒ x = ( 3 + √13 ) / 2 OR x = ( 3 - √13 ) / 2

∴ The roots of the quadratic equation are

x = ( 3 + √13 ) / 2 and x = ( 3 - √13 ) / 2.