Math, asked by anil4964, 1 month ago

Solve the following quadratic equation.
4√6x2−13x−2√6=0

Answers

Answered by varadad25
1

Question:

Solve the following quadratic equation.

4 √6 x² - 13x - 2 √6 = 0

Answer:

The roots of the quadratic equation are

x = 2 √6 / 3 OR x = - √6 / 8.

Step-by-step-explanation:

The given quadratic equation is

4 √6 x² - 13x - 2 √6 = 0.

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

  • a = 4 √6
  • b = - 13
  • c = - 2 √6

Now,

b² - 4ac = ( - 13 )² - 4 * 4 √6 * ( - 2 * √6 )

⇒ b² - 4ac = 169 - 16 * ( - 2 ) * √6 * √6

⇒ b² - 4ac = 169 + 32 * 6

⇒ b² - 4ac = 169 + 192

b² - 4ac = 361

By quadratic formula,

x = [ - b ± √( b² - 4ac ) ] / 2a

⇒ x = [ - ( - 13 ) ± √361 ) ] / ( 2 * 4 √6 )

⇒ x = ( 13 ± 19 ) / ( 8 √6 )

⇒ x = ( 13 + 19 ) / ( 8 √6 ) OR x = ( 13 - 19 ) / ( 8 √6 )

⇒ x = 32 / ( 8 √6 ) OR x = - 6 / ( 8 √6 )

⇒ x = 4 / √6 OR x = - 3 / 4 √6

By multiplying and dividing by √6, we get,

⇒ x = 4 / √6 * ( √6 / √6 ) OR x = - 3 / 4 √6 * ( √6 / √6 )

⇒ x = 4 √6 / ( √6 * √6 ) OR x = - 3 √6 / ( 4 √6 * √6 )

⇒ x = 4 √6 / 6 OR x = - 3 √6 / ( 4 * 6 )

⇒ x = 2 √6 / 3 OR x = - √6 / ( 4 * 2 )

⇒ x = 2 √6 / 3 OR x = - √6 / 8

The roots of the quadratic equation are

x = 2 √6 / 3 OR x = - √6 / 8.

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