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