Question

Find the roots of the following Quadratic Equations by factorisation.
2x2 + x - 6 = 0​

Answer 1

1st root is -2 and 2nd root is 3/2

Answer 2

EXPLANATION.

Quadratic equation.

⇒ 2x² + x - 6 = 0.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ 2x² + 4x - 3x - 6 = 0.

⇒ 2x(x + 2) - 3(x + 2) = 0.

⇒ (2x - 3)(x + 2) = 0.

⇒ x = 3/2  and  x = -2.

                                                                                                                           

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and different, 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.