Question

0.28. Find the roots of the following quadratic equation:
√3x² – 2√2x- 2√3=0 please give accurate and full explained solution​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ √3x² - 2√2x - 2√3 = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

⇒ D = (-2√2)² - 4(√3)(-2√3).

⇒ D = 4 x 2 + 4(√3)(2√3).

⇒ D = 8 + 4(6).

⇒ D = 8 + 24.

⇒ D = 32.

⇒ x = - b + √D/2a.

⇒ x = -(-2√2) + √32/(2√3).

⇒ x = 2√2 + 4√2/(2√3).

⇒ x = 6√2/(2√3).

⇒ x = 3√2/(√3). = √6.

⇒ x = - b - √D/2a.

⇒ x = -(-2√2) - √32/(2√3).

⇒ x = 2√2 - 4√2/(2√3).

⇒ x = - 2√2/(2√3).

⇒ x = -√2/√3.

                                                                                                                       

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.