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SOLUTIONS OF ALGEBRAIC EQUATIONS

 

SOLUTIONS OF ALGEBRAIC EQUATIONS

 
 
QUARTIC EQUATION: ax2+bx + c =0
 
 
  • Solutions:-
    If a, b, c are real and if D = b2-4ac is the discriminant, then the roots are
      • real and unequal if d > 0
      • real and equal if d = 0
      • complex conjugate if d < 0
    1. If xl,x2 are the roots, then xl + x2 =- b/a and xlx2 =c/a.
 
 

CUBIC EQUATION:  a3 + a1x2 + a2x + a3 = 0


If a1,a2, a3 are real and if D = Q3 + R2 is the discriminant, then

  1. one root is real and two complex conjugate if d > 0
  2. all roots are real and at least two are equal if d = 0
  3. all roots are real and unequal if d < 0.

If d < 0, computation is simplified by use of trigonometry.