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Solving quadratic equation by quadratic formula.pptx
- 1. Good Morning MATHEMATICS 9August 27, 2023
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- 3. OBJECTIVES Solve quadratic equationby quadratic formula
- 4. Derive the QuadraticFormula Applying the Method of Completing the Square
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- 8. What Does TheFormula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise. The formula states that for a quadratic equation of the form : ax2 + bx + c = 0 The roots of the quadratic equation are given by : 𝑥= −𝑏±√𝑏 2 −4𝑎𝑐 2𝑎
- 9. Example 1 Usethe quadratic formula to solve the equation : x 2 + 5x + 6= 0 Solution: x 2 + 5x + 6= 0 a = 1 b = 5 c = 6 𝑥= −𝑏± √𝑏 2 − 4 𝑎𝑐 2 𝑎 𝑥= −(5)± √(5) 2 −(4)(1)(6) (2)(1) 𝑥= −5±√25−24 2 𝑥= −5 ± √1 2 𝑥= −5+1 2 𝑜𝑟 𝑥= −5 −1 2 x = - 2 or x = - 3 These are the roots of the equation.
- 10. a = 8b = 2 c = -3 𝑥= −𝑏±√𝑏 2 −4𝑎𝑐 2𝑎 𝑥= −2±√2 2 −(4×8×−3) 2×8 𝑥= −2 ± √4 ❑ −(− 96) 16 𝑥= −2+10 16 𝑜𝑟 𝑥= −2−10 16 𝑥= −2+10 16 𝑜𝑟 𝑥= −2 −10 16 x = ½ or x = - ¾ These are the roots of the equation. Example 2 Use the quadratic formula to solve the equation : 8x 2 + 2x - 3= 0 Solution: 8x 2 + 2x - 3= 0
- 11. Example 3 Usethe quadratic formula to solve the equation : 8x 2 - 22x + 15= 0 Solution: 8x 2 - 22x + 15= 0 a = 8 b = -22 c = 15 𝑥= −𝑏± √𝑏 2 − 4 𝑎𝑐 2 𝑎 𝑥=−(−22)±√¿¿¿ 𝑥= 22 ± √(484 )−(480) 16 𝑥= 22 ± √4 16 𝑥= 22+2 16 𝑜𝑟 𝑥= 22− 2 16 x = 3/2 or x = 5/4 These are the roots of the equation.
- 12. Example 4 Usethe quadratic formula to solve for x: 2x 2 +3x - 7= 0 Solution: 2x 2 + 3x – 7 = 0 a = 2 b = 3 c = - 7 𝑥= −𝑏±√𝑏2 −4𝑎𝑐 2𝑎 𝑥= −3±√32 −(4 ×2×−7) 2×2 𝑥= −3 ± √9 −(−56) 4 𝑥= −3±√65 4 These are the roots of the equation. 𝑥= −3+√65 4 𝑜𝑟 𝑥= −3−√65 4
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