Math, asked by panikb9572, 1 month ago

Solve the following quadratic equation.
√3x2+10x+7√3=0

Answers

Answered by varadad25
0

Question:

Solve the following quadratic equation.

√3 x² + 10x + 7 √3 = 0

Answer:

The roots of the quadratic equation are

x = - √3 OR x = - 7 √3 / 3.

Step-by-step-explanation:

The given quadratic equation is

√3 x² + 10x + 7 √3 = 0.

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

  • a = √3
  • b = 10
  • c = 7 √3

Now,

b² - 4ac = ( 10 )² - 4 * √3 * 7 * √3

⇒ b² - 4ac = 100 - 4 * 7 * √3 * √3

⇒ b² - 4ac = 100 - 28 * 3

⇒ b² - 4ac = 100 - 84

b² - 4ac = 16

By quadratic formula,

x = [ - b ± √( b² - 4ac ) ] / 2a

⇒ x = ( - 10 ± √16 ) / ( 2 * √3 )

⇒ x = ( - 10 ± 4 ) / ( 2 √3 )

⇒ x = ( - 10 + 4 ) / ( 2 √3 ) OR x = ( - 10 - 4 ) / ( 2 √3 )

⇒ x = - 6 / ( 2 √3 ) OR x = - 14 / ( 2 √3 )

⇒ x = - 3 / √3 OR x = - 7 / √3

By multiplying and dividing by √3, we get,

⇒ x = - 3 / √3 * ( √3 / √3 ) OR x = - 7 / √3 * ( √3 / √3 )

⇒ x = - 3 √3 / ( √3 * √3 ) OR x = - 7 √3 / ( √3 * √3 )

⇒ x = - 3 √3 / 3 OR x = - 7 √3 / 3

x = - √3 OR x = - 7 √3 / 3

The roots of the quadratic equation are

x = - √3 OR x = - 7 √3 / 3.

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