Quadratic Equations – Part 1

Type 1: x^{2}+5x+6= 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

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