Sum and product of roots
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This document discusses finding the sum and product of the roots of quadratic equations. It provides the formulas for calculating the sum and product of roots without explicitly solving for the individual roots. The sum of the roots is equal to -b/a, and the product of the roots is equal to c/a, where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0. Several examples are worked out applying these formulas. The document also contains exercises asking the reader to find the sum and product of roots for additional quadratic equations using the given coefficients a, b, and c.
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