Quadratic Equations


   
 
Summary
 
  • 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 distinct
           ii) b2 - 4ac = 0 Roots are real and equal
           iii) 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.
 
 
     
   
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