Multiple choice

For what value of c the quadratic equation x2 – (c + 6) x + 2(2c – 1) = 0 has sum of the roots as half of their product?

  1. 5
    • 4

  3. 7

  4. 3
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C Correct answer
Explanation

Sum of roots = c + 6. Product of roots = 2(2c - 1) = 4c - 2. Given sum = 1/2 * product, so c + 6 = (4c - 2) / 2. c + 6 = 2c - 1, which gives c = 7.

AI explanation

Using Vieta's formulas for the equation x2 - (c + 6)x + 2(2c - 1) = 0, the sum of the roots is c + 6 and the product of the roots is 4c - 2. The problem states that the sum is half of the product, so c + 6 = 0.5(4c - 2). Simplifying this gives c + 6 = 2c - 1, which means c = 7.

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