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