Page 20 - CHAPTER 4 (Quadratic equations)

CHAPTER 4

QUADRATIC EQUATIONS

Sign of the Roots

Sign of (+) Sign of () Sign of ,

+ve +ve  and  are positive

-ve +ve  and  are negative

+ve -ve  is positive and  is negative , if >

-ve -ve  is negative and  is positive , if ||>||

and vice-versa

Nature of Roots

For a quadratic equation ax +bx+c=0 where a, b, c R ard a≠ 0 and
2
2
D=b -4ac

D=b -4ac
2

D<0 D0
Roots are imaginary or Roots are real
complex with non –zero
imaginary part

D=0 D>0
Roots are equal Roots are un equal
and rational

D is a perfect D is not a perfect
square square
↓ ↓
Roots are Roots are irrational
rational if a,b,c and conjugate pair if
are rational a, b, c are rational

20