Sum and product of roots
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Sum and product of roots
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Sum and product of roots
- 1. THE SUM AND THE PRODUCT OF ROOTS OF QUADRATIC EQUATIONS Ms. Majesty P. Ortiz
- 5. − 𝟏 𝟐 𝟒 𝟐 − 𝟒 𝟑 − 𝟐 𝟑 𝟖 𝟗𝒙 + 𝟐 𝒙 − 𝟐𝒙 𝟐 − 𝟒(𝒙 − 𝟓)(𝒙 + 𝟓)𝒙 𝟐 -25
- 6. Quadratic Equation Roots Sum of Roots Product of Roots 𝑥2 + 7𝑥 + 12 = 0 𝑥2 + 7𝑥 − 18 = 0 𝑥2 − 5𝑥 − 24 = 0 4𝑥2 + 𝟖𝑥 + 𝟑 = 0 2𝑥2 + 8𝑥 − 10 = 0 8𝑥2 − 𝟔𝑥 − 𝟗 = 0
- 7. x = −𝒃± 𝒃 𝟐−𝟒𝒂𝒄 𝟐𝒂 𝒙 𝟏 = −𝒃 + 𝒃 𝟐 − 𝟒𝒂𝒄 𝟐𝒂 𝒙 𝟐 = −𝒃 − 𝒃 𝟐 − 𝟒𝒂𝒄 𝟐𝒂
- 8. Sum of the Roots of Quadratic Equation 𝒙 𝟏 + 𝒙 𝟐 = −𝒃 𝒂 Product of the Roots of Quadratic Equation 𝑥1 ⋅ 𝑥2 = 𝑐 𝑎
- 9. 1) 𝒙 𝟐 −𝟐𝒙 − 𝟑 = 𝟎 2) 𝟔𝒙 𝟐 + 𝟏𝟐𝒙 + 𝟒 = 𝟎 3) 𝟗𝒙 𝟐 − 𝟐𝟓 = 𝟎
- 10. Use the values of a, b, and c of each of the following equations in determining the sum and the product of its roots. 1. 𝒙 𝟐 +𝟒𝒙 + 𝟑 = 𝟎 2. 𝟔𝒙 𝟐 + 𝟏𝟐𝒙 − 𝟏𝟖 = 𝟎 3. 𝒙 𝟐 +𝟒𝒙 − 𝟐𝟏 = 𝟎 4. 𝟐𝒙 𝟐 + 𝟑𝒙 − 𝟐 = 𝟎 5. 𝟑𝒙 𝟐 − 𝟏𝟎𝒙 − 𝟖 = 𝟎
- 11. SUM PRODUCT 1. - 4 3 2. -2 -3 3. -4 -21 4. − 𝟑 𝟐 -1 5. 𝟏𝟎 𝟑 − 𝟖 𝟑
- 12. A.Without solving for the roots, find the sum and product of the roots of each quadratic equation. 1. 𝒙 𝟐 + 𝟓𝒙 − 𝟔 = 𝟎 2. 𝒙 𝟐 +𝟏𝟓𝒙 + 𝟓𝟒 = 𝟎 3. 𝒙 𝟐 +𝟖𝒙 = −𝟏𝟑 4. 𝟑𝒙 𝟐 + 𝟔𝒙 − 𝟑 = 𝟎 5. 𝟒𝒙 𝟐 + 𝟖𝒙 + 𝟑 = 𝟎 B.Write a quadratic equation with integral coefficients whose sum and product of roots are given. 1. 𝟏 𝟐 𝒂𝒏𝒅 − 𝟐 𝟑 2. − 𝟑 𝟒 𝒂𝒏𝒅 𝟓 𝟔 3. 0 and 6