REDUCIBLE QUADRATIC EQUATIONS
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The document discusses solving equations that are reducible to quadratic equations. It explains that a quadratic equation is an equation with a maximum power of the variable being squared. There are three methods for solving quadratic equations: factorization, completing the square, and the quadratic formula. Examples are provided of using factorization and completing the square methods to solve equations reducible to quadratic form. The document also covers forming quadratic equations from word problems and solving them.
REDUCIBLE QUADRATIC EQUATIONS
- 1. SUBJECT : MATHEMATICS CHAPTER ( 2/4 ) : EQUATIONS LESSON NO : 04 OF 09 TOPIC : SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION
- 3. Q. What do you mean by an equation ? A. An equation is a statement in which two quantities are equal. Q. What do you mean by quadratic equation? A. An equation in one variable and maximum power of that variable is two is called quadratic equation. Q. How many techniques to solve quadratic equations? A. There are three basic techniques to solve a quadratic equation: (i) Factorization method (ii) Completing square method (iii) Quadratic formula
- 4. SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION First Form Second Form 0 fx e dx c bx a fd,b,x c y b ay 0y
- 5. Solve Solution Multiplying both sides by (x + 1) (x-1) 5 (x-1) +3 (x+1) = 6 (x+1)(x-1) 5x – 5 + 3x + 3 = 6x2 – 6 6 1x 3 1x 5 Example SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION
- 6. 8x – 2 = 6x2 – 6 6x2 - 8x – 6+ 2 = 0 6x2 – 8x – 4 = 0 3x2 - 4x – 2 = 0 SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION We Know that a2 ac4bb x 2
- 7. 6 234164 x 6 24164 x 3 102 6 404 x SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION Putting the values of co- efficient in the formula
- 8. Solution Let 14x 14x y Then the given equation can be written in the form 3 10 y 1 y SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION 3 1 3 14x 14x 14x 14x Example Solve (i)
- 9. 3y2 – 10y + 3 = 0 3y2 – 9y – y + 3 = 0 3y(y-3) - 1(y – 3) = 0 (3y – 1)(y – 3) = 0 (3y –1) = 0 and (y – 3) = 0 SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION
- 10. 3 1 y or y = 3 Now by substituting the values of y in (i), we have 3 1 14x 14x 3 14x 14x and 2 1 x 2 1 x and Therefore the solution set is 2 1 , 2 1 SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION
- 11. SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION First Form Second Form 0 fx e dx c bx a fd,b,x c y b ay 0y
- 13. Assignment 1,0x; 2 5 x 1x 1x x 4 17 13x 1 13x (a) (b) SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC EQUATION
- 14. SOLUTION OF EQUATIONS REDUCIBLE TO QUADRATIC FORM