Solve the quadratic equation x² + 5x + 6 = 0

We will split the middle term to solve this quadratic equation.

Answer: The roots of the quadratic equation x² + 5x + 6 = 0 are -2 and -3

Let us see how to factorize the quadratic equation.

Explanation:

We will factorize x² + 5x + 6 by splitting the middle term.

First, we need to find two numbers ‘a’ and ‘b’ such that a + b = 5x and ab = 6x²

We know that 3x + 2x = 5x and 3x × 2x = 6x²

Thus, we can rewrite the equation x² + 5x + 6 as

= x² + 3x + 2x + 6

Taking the common factor x out from the first 2 terms we have:

x² + 3x = x (x + 3)

Now, taking the common factor 2 out from the third and 4th term

2x + 6 = 2 (x + 3)

Thus, x² + 5x + 6

=x² + 3x + 2x + 6

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

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

x² + 5x + 6= (x + 3)(x + 2)

So, (x + 3) and (x + 2) are the factors of the polynomial x² + 5x + 6.

To find the roots,

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

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