QUADRATIC EQUATIONS

QUADRATIC EQUATIONS

1. Standard form of the quadratic equation :- ax +bx+c=0, where a=0

   • Any equation of the form P(x)=0, where P(x) is a polynomial of degree 2 is a quadratic equation

2. ZEROES/ROOTS OF QUADRATIC EQUATION

   • A quadratic equation has almost two roots/zeroes.

3. RELATION BETWEEN ZEROES & COEFFICIENT OF A QUADRATIC EQUATION

   • If α&β are zeroes of the quadratic equation ax +bx+c=0, where a,b,c are real numbers and a=0, then
     • α+β=(-b)/a. => sum of zeroes= (-coefficient of x)/coefficient of x
     • product of zeroes= constant term/coefficient of x. αβ=> c/a

4. METHODS OF SOLVING QUADRATIC EQUATION

   • i) Factorisation
   • ii) Completing the square
   • iii) Quadratic formula

5. METHODS OF FACTORISATION

   • In this method we find the roots of a quadratic equation by factorising LHS into 2 linear factors and equating the factor to zero
   • The middle term is split into two whose product is equal to the 1st & last term of the equation

6. QUADRATIC FORMULA

   • Of an equation ax +bx+c=0, if b -4ac >= 0, then the roots of the above equation are given by: x= -b+-square root(b -4ac)/2a

7. NATURE OF ROOTS:

   • For Quadratic equation ax +bx+c=0 (a=0), value of(b -4ac) is called discrimination of the equation and is denoted as ‘D’
     • I) If D=0, then roots are real and equal
     • ii) If D>0, then roots are real and unequal
     • If D<0, then roots are not real