Question

Factorise the following : x²–2√3x–24​

Answer 1

$</p><p></p><p> </p><p>x </p><p>2</p><p> +4 </p><p>3</p><p> </p><p> x−2 </p><p>3</p><p> </p><p> x−24 \\ =x∣x+4 </p><p>3</p><p> </p><p> ∣−2 </p><p>3</p><p> </p><p> x×∣x+4 </p><p>3</p><p> </p><p> ∣</p><p> \\ =∣x+4 </p><p>3</p><p> </p><p> ∣∣x−2 </p><p>3</p><p> </p><p> ∣$

Answer 2

EXPLANATION.

Factorizes : x² - 2√3x - 24.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² - 4√3x + 2√3x - 24 = 0.

⇒ x(x - 4√3) + 2√3(x - 4√3) = 0.

⇒ (x + 2√3)(x - 4√3) = 0.

⇒ x = - 2√3  and  x = 4√3.

                                                                                                                 

MORE INFORMATION.

Nature of the roots of 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.