Short Tricks to Solve Quadratic Equations

  • An equation is a statement of equality between two expressions which is not true for all values of the variable involved.
  • A polynomial in which maximum power of variable is two is called quadratic equation. General form of quadratic equation is  where a, b and c are real numbers and x is a variable and a ≠ 0.

Roots of a Quadratic Equation:

  • The values of variable which satisfies the quadratic equation is called solution of the quadratic equation or the roots of the equation.
The roots of quadratic equation is is:

whereis called discriminant of the quadratic equation and it is represented by D.

Solution of a Quadratic Equation:

(i) By Factorisation Method: 

if the factors of the given equation  is such that 
(dx + e) (fx + g), d≠0, f≠0
Then, (dx + e) (fx + g) = 0
dx = -e or fx = -g
Hence,  are the roots of given equation.

(ii) By Shreedharacharaya formula: 

The following formula could be used for equation :

If roots of the quadratic equation is α , β , then

Nature of Roots of Quadratic Equation :

The nature of roots of the quadratic equations are dependent upon the discriminant

D =  , the following table will be helpful to find the nature of roots of a quadratic equation:

Also, if roots of the quadratic equation  is α, β, then

Sum of roots, and product of roots, 

Problem Solving Tricks :

  • If α and β are the given roots of the quadratic equation , then you can form the equation as;

  • When one root of equation is zero, then constant term will be zero.
  • Product of roots =i.e c = 0
  • If the term containing x and constant term are both zero simultaneously, then both roots of the equation are zero.
  • If coefficient of   and constant term are equal , then both the roots of equation are reciprocal of each other.
  • If there is no term containing coefficient of x, then both the roots of the equation are equal in magnitude but opposite in sign.
  • If b is of opposite sign as compared to a and c , then both roots are positive.
  • If a, b ,c are all of the same sign, then both the roots are negative.
  • If a and c are of opposite signs, then both the roots of the equation are of opposite sign.

Symmetrical Functions of Root :

Let the roots of an equation  are α and β, then 
   Good Luck!                                                                                                           

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