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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.
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
Thus, the solutions of the quadratic equation x2 + 5x + 6 = 0 are x = -2 and x = -3.