# Solve the quadratic equation x^{2} + 5x + 6 = 0

We will use splitting the middle term method to solve this.

## Answer: Solving the quadratic equation x^{2} + 5x + 6 = 0 ,we get the roots x = -2, -3

Let see, how we can factorize the quadratic equation.

**Explanation: **

We will factor x^{2} + 5x + 6 by splitting the middle term.

Firstly, we need to find two numbers ‘a’ and ‘b’ such that a + b = 5(coefficient of x) and ab = 6(the constant term) .

we know that 3 + 2 = 5 and 3 times 2 = 6

Thus, we can rewrite the equation x^{2} + 5x + 6 as

= x^{2} + 3x + 2x + 6

taking the common factor x out from the first 2 terms we have

x^{2} + 3x = x (x+3)

now taking the common factor 2 out from the third and 4th tern

2x+6 = 2 (x+3)

Thus, x^{2} + 5x + 6

=x^{2} + 3x + 2x + 6

= x(x + 3) + 2(x + 3)

Now we see that (x+3) is common ,taking the common factor out, we get

x^{2} + 5x + 6= (x + 3)(x + 2)

So, (x + 3) and (x + 2) are the factors of the polynomial x^{2} + 5x + 6.

to find the roots , we just equate (x + 3)(x + 2)to -

==> x+3 =0 and x+2 = 0

==> x = -3 and x= -2