Simplest method to solve quadratic equation

1. Quadratic
Equation
Simplest Method
to solve

2. A
Sum of the coefficients in EQUATION is a+b+c
To learn this trick first you need to understand the basic of Quadratic trinomial.
Quadratic trinomial is product of two linear binomials as show below
Product of the sum of the coefficients of the factors = Sum of the coefficients in the product
The trick is
First Step
Second Step
Third Step
Calculate RHS of above equation
Product of Coefficient of factors
So (M+p)(N+q)= a+b+c
Find M,N,p and q so that
M*N=A and P*Q=C
Simplest Method to Solve Quadratic Equation
Here product of coefficient is
ax +bx+c=(Mx+p)(Nx+q)2
(Mx+p)(Nx+q)
(M+p)(N+q)

3. Sum of a, b and c
First write a, b and c coefficients of quadratic trinomial given so you can use them later
Then find sum of a, b, and c
x2+5x+6=0
Easy Equation
Step 2:
These steps seems complex, let’s go through some problems to
understand how easy they are
ax2+bx+c=0
x2+5x+6=0
a=1,b=5,c=6
→ a+b+c=1+5+6=12
Convert equation into (m+p)(n+q) form. To do this first find M and N
Here equation can be written as
1 * x2+5 * x+6=0
Now break a into multiplication of two integers and c=6
a=1=1 * 1=m * n
So m=1, n=1
(M+p)(N+q)= a+b+c
(1+p)(1+q)= 12

4. Step 3:
Now we can find p and q but ensure that p*q=c .12 can be written as multiplication of two integers
1 x 12 =12
(1+0) x (1+11) =12
p=0 ,q=11 p*q=0*11≠6
2 x 6 =12
(1+1) x (1+5) =12
p=1,q=5 p*q=1*5≠6
3 x 4 =12
(1+2) x (1+3) =12
p=2,q=3 p*q=6=c
The equation is
(1+2)(1+3)=12
m=1,n=2,p=2,q=3 so the solution is
(x+2)(x+3)=x2+5x+6

5. Tough Equation:
Step 1:
Step 2:
Now let’s take a tough problem
6x2+15x+6=0
Find a, b c and their sum
ax2+bx+c=0
6x2+15x+6=0
a=6,b=15,c=6
a+b+c=6+15+6=27
Convert equation into (m+p)(n+q) form
Now break a into multiplication of two integers and here c=6
a=6=1*6=m*n
So m=1, n=6
(M+p)(N+q)= a+b+c
(1+p)(6+q)= 27

6. Now we can find p and q but ensure that p*q=c=6
Now 27 can be written as multiplication of two integers
1 x 27 =27
(1+0) x (1+26) =27
p=0 ,q=26
p*q=0*11≠6
3 x 9 =27
(1+2) x (6+3) =27 p=2,q=3
p*q=2*3=6=c
The equation is m=1,n=6,p=2,q=3
The solution is
(x+2)(6x+3)=6x2
+15x+6