Quadratic equations

Quadratic equations

1. Definition

   • Equation of second degree
   • Includes a squared term
   • general form
     • ax² + bx + c = 0
       • a,b,c are constants
       • x is a variable
       • a≠0
     • not unique
       • x² + 2x + 3 = 0
       • 2x² + 4x + 6 = 0
       • Same
   • Highest degree: 2

2. Roots

   • solution of quadratic equations
   • x-intercepts of the quadratic function
   • nature of roots
     • discriminant
       • b²-4ac
       • > 0
         • 2 Distinct real roots
       • = 0
         • Repeated real roots
       • < 0
         • No real roots
       • Δ

3. Solving quadratic equations

   • Factoring
     • identities
     • cross method
     • take out common factor
   • quadratic formula
     • completing square
       • substitution
     • x = [-b ± √(b² - 4ac)] / 2a
   • taking square root
   • graphical method
     • approximations only

4. Word problems

   • Let unknown
   • Set up equation
   • Solve equation
   • Reject
   • Check by substitution into the word problem
   • Conclusion

5. in one unknown x

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