QUADRATIC EQUATIONS - created from Mind Map

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

ZEROES/ROOTS OF QUADRATIC EQUATION

RELATION BETWEEN ZEROES & COEFFICIENT OF A QUADRATIC EQUATION

METHODS OF SOLVING QUADRATIC EQUATION

METHODS OF FACTORISATION

QUADRATIC FORMULA

NATURE OF ROOTS:

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

A quadratic equation has almost two roots/zeroes.

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

i) Factorisation

ii) Completing the square

iii) Quadratic formula

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

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

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