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Quadratic equation slideshare
- 1. JSS MAHAVIDYAPEETA MYSURU 4 JSS INSTITUTE OF EDUCATION Sakleshpur 573134 ANUSHA RANI A B.ED 2nd SEMESTER REG.NO: ED190306 JSS INSTIUTUTE OF EDUCATION SAKLESHPUR
- 4. INTRODUCTION CONTENT Definition of quadratic equation Examples Hidden quadratic equation Methods of solution 1. Factorization
- 5. DEFINITION In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is ax2 + bx + c=0 Where x represents a variable or an unknown and a, b and c are constants with a≠0. If a=0?? Then the equation is a linear equation
- 6. IMPORTANCE The general form is ax2 + bx + c = 0 The expression on the right hand side ax2+ bx+ c is called as a quadratic expression. The name quadratic comes from quad ,meaning square ,because the variable gets squared like x2. A quadratic equation is a trinomial expression. Why??? Because in standard form it adds three terms ax2 , bx and c.
- 7. More examples of quadratic equation 2x2+ 5x+ c=0 In this one a=2,b=5 c=3. x2_ 3x=0 This one is little more tricky; Where is a? In fact a=1, as we don't usually write “1x2” b= -3 and where is c? well, c=0 is not shown. 5x- 3=0 Oops! This one is not be quadratic equation because it is missing x2 (in other Words if a=0 and that means it cant be quadratic).
- 8. METHODS OF SOLUTION The methods of solving quadratic equation is : • Factorization
- 9. Ex: Solve x2 + 7x + 6 = 0 Quadratic equation factor the left hand side (LHS) x2 + 7x + 6 = (x + 6 )(x + 1) x2 + 7x + 6 = (x + 6)(x + 1) = 0 Now the equation as given is of the form ab = 0 set each factor equal to 0 and solve x + 6 = 0 x + 1 = 0 Solution: x = - 6 and – 1 x = {-6, - 1}
- 10. Method 1: Factorization Q : Factorize ax2+ bx+ c If ax2+ bx+ c = (rx + p)(sx + p) = 0 Then the solutions of the equation are x1 = -p/r x2 = -q/s Example: x2 -2x -15=0 (x - 5) (x + 3)=0 x =5 x=-3 -15 x2 -5 +3 2 2
- 11. Any questions . . .