Solve the quadratic equation x2 + 5x + 6 = 0
We will use splitting the middle term method to solve this.
Answer: Solving the quadratic equation x2 + 5x + 6 = 0 ,we get the roots x = -2, -3
Let see, how we can factorize the quadratic equation.
We will factor x2 + 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 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 tern
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 , we just equate (x + 3)(x + 2)to -
==> x+3 =0 and x+2 = 0
==> x = -3 and x= -2