Sum and product of the roots of a
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The document discusses how to find the sum and product of the roots of a quadratic equation ax^2 + bx + c = 0. It provides the formulas that the sum of the roots is equal to -b/a and the product of the roots is equal to c/a. It then works through two examples of using these formulas to find the sum and product of the roots of equations 3x^2 + 4x - 5 = 0 and 4x^2 - 29x - 24 = 0. The solutions show the steps of identifying a, b, c and then applying the formulas to determine the sum and product of the roots for each example equation.
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Sum and product of the roots of a
- 1. Sum and Product of the Roots of a Quadratic Equation Ms G. Martin
- 2. The sum and product of the roots of a quadratic equation ax2 + bx + c = 0 is determined by : Sum (x1 + x2) = - 𝒃 𝒂 and Product (x1 . X2) = 𝒄 𝒂
- 3. Example 1. Find the sum and product of the roots of the equation 3x2 + 4x – 5 = 0 Steps Solution 1. Identify the values of a, b, and c. a = 3, b = 4, c = -5 2. Determine the sum of the roots of 3x2 + 4x – 5 = 0 x1 + x2 = - 𝒃 𝒂 = - 𝟒 𝟑 3. Determine the product of the roots 3x2 + 4x – 5 = 0 x1 . x2 = 𝒄 𝒂 = −𝟓 𝟑
- 4. Steps Solution 4. Verified the obtained sum and product using the form x2 – (x1 + x2)x + (x1 . x2) = 0 x2 – (- 4 3 )x - 5 3 = 0 = x2 + 𝟒 𝟑 x - 𝟓 𝟑 = 0 5. Check when simplifying quadratic equation. 3x2 + 4x – 5 = 0 3x2 3 + 4x 3 - 5 3 = 0 = x2 + 𝟒 𝟑 x - 𝟓 𝟑 = 0 So, the sum and product of the roots of 3x2 + 4x – 5 = 0 are - 𝟒 𝟑 and −𝟓 𝟑 respectively.
- 5. Example 2. Find the sum and the product of the roots of the equation 4x2 – 29x – 24 = 0 Steps Solution 1. Identify the values of a, b, and c. a = 4, b = -29, c = -24 2. Determine the sum of the roots of 4x2 - 29x – 24 = 0 x1 + x2 = - 𝒃 𝒂 = -( −29 4 ) = 𝟐𝟗 𝟒 3. Determine the product of the roots 4x2 - 29x – 24 = 0 x1 . x2 = 𝒄 𝒂 = −𝟐𝟒 𝟒 = -6