# Formula To Solve Quadratic Equation Problems

## Formulas for Quadratic Equations & Definitions

An equation where the highest exponent of the variable is a square. Standard form of quadratic equation is ax2+bx+c = 0

Where,  x is the unknown variable and a, b, c are the numerical coefficients.

If ax2+bx+c = 0 is a quadratic equation, then the value of x is given by the following formula

x = [(-b ± √(b2-4ac))/2a] ### Factorization

• It is very simple method to to solve quadratic equations. Factorization give 2 linear equations
For example, x2 + 3x – 4 = 0

Here, a = 1, b = 3 and c = -4

Now, find two numbers whose product is – 4 and sum is 3.

So, the numbers are 4 and -1.

Therefore, two factors will be 4 and -1

### Completing the Square Method

• Every Quadratic question has always a square term. If we could get two square terms of quality sign we can get a linear equations. Middle term is called as ‘b’ and splited by (b/2)²

For example – x²+ 6x +7

Here x² =1, b= 4
(b/2)² = (4/2)² = 4
x²+4x+4 = -1+4
(x+2)² = 3
Take the square of both side
x+2 = ±√3  = ± 1.73
Therefore, x = -0.27 or -3.73

### Formulas of Quadratic Equations & Key points to Remember

Other basic concepts to remember while solving quadratic equations are:

#### 1.Nature of roots

Nature of roots determine whether the given roots of the equation are real, imaginary, rational or irrational. The basic formula is b² – 4ac.

This formula is also called discriminant or D. The nature of the roots depends on the value of D. Conditions to determine the nature of the roots are:

If D < 0, than the given roots are imaginary.

If D = 0, then roots given are real and equal.

If D > 0, then roots are real and unequal.

Also, in case of D > 0, if the equation is a perfect square than the given roots are rational, or else they are irrational.

#### 2. Sum and product of the roots

For any given equation the sum of the roots will always be -b/a, and the product of the roots will be c/a. Thus, the standard quadratic equation can also be written as x2 – (Α + Β)x + Α*Β = 0