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Quadratic Equations

Quadratic Equations. 3 rd Year Maths October 4 2012 Classes Plath & Shelley. Today We will be continuing on with…. ‘Quadratic Equations’ What are they? How do they look? How do we solve them?. From the last Day. A quadratic eqn is an eqn in the form of: Where a, b and c are constants.

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Quadratic Equations

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  1. Quadratic Equations 3rd Year Maths October 4 2012 Classes Plath & Shelley

  2. Today We will be continuing on with…. • ‘Quadratic Equations’ • What are they? • How do they look? • How do we solve them?

  3. From the last Day • A quadratic eqn is an eqn in the form of: • Where a, b and c are constants. • Solving a quadratic eqn means finding the two values of the variable (x) which satisfy the eqn. • These values are called roots. • There are three types of Quadratic eqn that we will encounter: • x2 – 5x – 14 = 0……..Three Terms • 2x2 – 9x = 0……...No constant term • 4x2 – 25 = 0……...No ‘x’ term

  4. From the last Day Method for solving Quadratic Equations Step 1: Bring every term to the left hand side. If necessary, multiply both sides by -1 so as to make the x2 term positive Step 2: Factorise the left hand side (Usually Two sets of brackets) Step 3: Let each factor = 0 Step 4: Solve each simple equation Example(Type 1: Three terms) Solve, x2 – 5x = 14 x2 – 5x – 14 = 0 …..all terms to the left hand side (x – 7)(x + 2) = 0 …..factorise x – 7 = 0 x + 2 = 0 …..let each factor equal 0 x = 7 x = -2 ….solve each equation Therefore: x = 7orx = –2

  5. More Examples Example:(Type2: No constant term) 2x2 – 9x = 0 x(2x – 9) = 0 ….factorise x = 0 x = 0 Example:(Type3: No ‘x’ term) 4x2 – 25 = 0 (2x – 5)(2x + 5) = 0 ….factorise (the difference of two squares) 2x - 5 = 0 2x = 5 x = 2x – 9 = 0 2x = 9 x = 2x + 5 = 0 2x = -5 x = - Answer: x = 0 or x = Answer: x = or x = -

  6. More Examples Example: 5x2 + 3x = 2 5x2 + 3x – 2 = 0 (5x - 2)(x + 1) = 0 …..trial and error To check, multiply the brackets out and you should get 5x2 + 3x – 2 5x – 2 = 0 x + 1 = 0 5x = 2 x = -1 x = Example: Q41 pg 32 6x(x -1) + 2 = x(3 – 4x) 6x2 - 6x + 2 = 3x - 4x2 6x2 - 6x + 2 - 3x + 4x2 = 0 10x2 -9x + 2 = 0 (5x - 2)(2x - 1) = 0 5x – 2 = 0 2x - 1 = 0 5x = 2 2x = 1 x = x = Answer: x = or x = -1 Answer: x = or x =

  7. Class Work • Complete Question 26, 38 & 42 on page 31. • Any questions, Ask!

  8. Class Work Correction

  9. Quadratic Equations in Fractional Form • Rules: • Multiply each part of the equation by the LCM of the expressions on the bottom. • Simplify both sides (cancel terms, no fractions left) • Proceed with the sum as normal…. • Step 1: Bring every term to the left hand side. If necessary, multiply both sides by -1 so as to make the x2 term positive • Step 2: Factorise the left hand side (Usually Two sets of brackets) • Step 3: Let each factor = 0 • Step 4: Solve each simple equation

  10. Quadratic Equations in Fractional Form Example 1(Q8 pg 33)

  11. Quadratic Equations in Fractional Form Example 2(Q5 pg 33)

  12. Class Work!!! • Complete Questions 1, 3, 12 on page 33. • Any questions, Ask!

  13. Class Work Correction

  14. Homework…

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