# Quadratic Equations – Part 1

Type 1: $x^{2}+5x+6=&space;0$,  Find the roots for the equation?

Basic method:

$x^{2}+5x+6$

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

$x(x+3)+2(x+3)$

$(x+2)(x+3)$

$x+2=0$            $x+3=0$

$x=-2$                $x=-3$

Short Cut Method:

• Step1: Find the factors for constant (In the given equation it is 6)
• 2,3,6,1 are the factors for 6
• Step 2: Select the factors such that when we  add we should get middle number (5 in the given equation) and when we multiply we should get constant (6).
• 2 and 3 are such factors which will give sum as 5 and multiplication as 6.
• If we take 1 and 6, multiplication is 6  but the sum is 7 which is not equal to 5.
• So the appropriate factors for the given equation are 3 and 2.
• Step 3: Change the sign  for the  factors
• Since it is ”+5x” in the given equation we need to change the sign for the factors  i.e. -3,-2
• If it is “-5x” in the equation we need to change the sign for the factor as 3, 2.

Note: 2 and 3 are co-primes. So we should select co-prime factors.

Observe the below diagram