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Revision - Quadratic Equations

Revision - Quadratic Equations. Solving Quadratic equations by the Quadratic Formula. By I Porter. For any quadratic equation ax 2 + bx + c = 0, where a ≠ 0,. Quadratic formula, a ≠0. Introduction.

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Revision - Quadratic Equations

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  1. Revision - Quadratic Equations Solving Quadratic equations by the Quadratic Formula. By I Porter

  2. For any quadratic equation ax2 + bx + c = 0, where a ≠ 0, Quadratic formula, a ≠0. Introduction The complete the square method of solving quadratic equations can be used to derive a formula to solve any quadratic equation. Proof: (not required for examination) For any quadratic equation ax2 + bx + c = 0, where a ≠ 0 Factorise LHS Rearrange RHS Divide throughout by ‘a’ Rearrange Take √ of both sides. If the term to complete the square LHS. Rearrange, x = ..

  3. For ax2 + bx + c = 0, then Example 1: Use the quadratic formula to solve. Always test on one you can factorise! x2 + 6x + 8 = 0 Write-out the substitution into formula a = +1, b = +6, c = +8 Evaluate as an exact value! Note: b2 - 4ac ≥ 0 for ax2 + bx + c = 0 to have solutions. This is called the discriminant.

  4. For ax2 + bx + c = 0, then Example 2: Use the quadratic formula to solve. 3x2 - 6x + 2 = 0 Write-out the substitution into formula a = +3, b = -6, c = +2 Evaluate as an exact value! Reduce all surds. Note: b2 - 4ac ≥ 0 for ax2 + bx + c = 0 to have solutions. This is called the discriminant.

  5. Evaluate as an exact value! For ax2 + bx + c = 0, then Quadratic Equation. Write-out the substitution into formula Correct to 2 decimal places. a = +1, b = -1, c = -1 Example 3: Use the quadratic formula to solve. Rearrange. You may have to give your answer correct a set number of decimal places or significant figures using your calculator to give an approximation.

  6. e) Exercise: Find exact solution to the following. a) x2 + 8x - 9 = 0 b) 2x2 - 6x - 5 = 0 c) 5x2 - x - 2 = 0 d) 4x2 - x - 1 = 5x + 4

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