A Quadratic Equation is the equation that can be rearranged in standard form ax2 + bx + c = 0 as where x is a variable and a, b, and c represent constants , where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term. ### 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 = $\frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$

• 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 $(\frac{b}{2})^2$

For example :  – x²+ 6x +7

Here x² =1, b= 4

$(\frac{b}{2})^2$ = $(\frac{4}{2})^2$ = 4

x²+4x+4 = -1+4

(x+2)² = 3

Take the square of both side

x+2 = ±$\sqrt{3}$ = ± 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  $– \frac{b}{a}$, and the product of the roots will be  $– \frac{c}{a}$. Thus, the standard quadratic equation can also be written as x2 – (Α + Β)x + Α*Β = 0