Question

factorise $x^2 - x - 6$ by using factor theorem.


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Answer 1

EXPLANATION.

Factorizes :

⇒ x² - x - 6 = 0.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² - 3x + 2x - 6 = 0.

⇒ x(x - 3) + 2(x - 3) = 0.

⇒ (x + 2)(x - 3) = 0.

⇒ x = - 2  and  x = 3.

                                                                                                                   

MORE INFORMATION.

Nature of roots of the quadratic expression.

(1) Roots are real and unequal, if b² - 4ac > 0.

(2) Roots are rational and different, if b² - 4ac is a perfect square.

(3) Roots are real and equal, if b² - 4ac = 0.

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

Answer 2

⇒ x² - x - 6 = 0

⇒ x² - 3x + 2x - 6 = 0

⇒ x(x - 3) + 2(x - 3) = 0

⇒ (x - 3)(x + 2) = 0

⇒ x = 3 , -2