Question

5. Factorize x2 +5x+6=0​

Answer 1

EXPLANATION.

Factorizes.

⇒ x² + 5x + 6 = 0.

Factorizes 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 the factors 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.

Answer 2

Question:

$\bf{Factorize \: x^2 +5x+6=0​}$

★ Concept:

Here, the concept of factorization method is used. Here, we are going to split the middle term.

Let's do it!

$\bf{x^2 +5x+6=0​}$

Here, 5x can be written as 3x + 2x

• If you add, you will get the middle term
• If you multiply, you will get $\bf{6x^2}$

$\implies\bf{x^2 +3x+2x+6=0​}$

On taking x and 2 as common factors, we get:

$\implies\bf{x(x+3)+2(x+3x)=0}$

$\implies\bf{(x+2)(x+3)=0}$

Hence, factorized.

Further, to find the roots:

$\bf{x+2 = 0 \: and \: x+3 = 0}$

$\implies\boxed{\bf{x = -2,-3}}$