Quadratic Equations - Nature of Roots


Ask a Question, Get an Answer!
Hundreds of tutors are online and ready to help you right now!
  • i) An expression of the form a0xn + a1xn-1+....+ an = 0, where n is a positive integer and a0, a1,...,an belong to some number system F, is called a polynomial in the variable x over F.
  • ii) The degree of polynomial is defined as the highest index of the variable x occurring in the polynomial.
i) An identity is a statement of equality between two expressions which is true for all values of the variable involved.

ii) An equation is a statement of equality between two expressions which is not true for all values of the variable involved.

  • If f(x)=0 is a polynomial equation and f(a)=0, then 'a' is a root of the polynomial equation.

If ax2 + bx + c = 0, a = 0, then  where a, b, c be any complex numbers.

  • A quadratic equation has exactly two roots.
  • For the quadratic equations, we have
i) b2 - 4ac > 0 Roots are real and distinctii) b2 - 4ac = 0 Roots are real and equaliii) b2 - 4ac < 0 Roots are imaginary and distinct
  • If the roots of ax2 + bx + c = 0, a(¹ 0),b, c Î R, are a and b, then
  • An expression in a, b is called a symmetric function of a, b if the expression is not affected by interchanging a and b.
  • The quadratic equation with roots a and b is given by x2- Sx + P = 0 where S = a + b and P = ab.


Ask a Question? Get an Answer!

connect to a tutor


Related Searches

quadratic equations summary

;,  

roots of polynomial equation

,  

formation of quadratic equation

,  

quadratic expression

,  

quadratic equations

,  

quadratic equations

,  

quadratic equation

,  

theory of quadratic equation

,  

quadratic function

,  

introduction quadratic function

,  

quadratic

,  

quadratic equations introduction

,  
symmetric functions
,  
some important definitions
,  
imaginary numbers
,  
math imaginary numbers
,  
polynomial
,  
Formation of quadratic equations from given complex roots and conditions
...more