Multiple choice

If the roots x1 and x2 of the quadratic equation satisfy the condition 7x2 – 4x1 = 47. The quadratic expression is x2 – 2x + c = 0, find the value of c.

  1. – 15

  2. 15

  3. -6

  4. None of these
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A Correct answer
Explanation

Roots x1, x2 satisfy x1+x2 = 2 and x1*x2 = c. We have 7x2 - 4x1 = 47 and x1+x2 = 2. Solving this system: x1 = 2-x2, so 7x2 - 4(2-x2) = 47 -> 11x2 = 55 -> x2 = 5. Then x1 = -3. Product c = x1*x2 = -15.

AI explanation

From the quadratic expression x^2 - 2x + c = 0, the sum of the roots x1 and x2 is 2 by Vieta's formulas, so we can express x1 as 2 - x2. Substituting this into the condition 7x2 - 4x1 = 47 gives 7x2 - 4(2 - x2) = 47, which simplifies to 11x2 - 8 = 47, meaning x2 = 5. Since the roots add to 2, x1 must be -3, and the product of the roots (x1 * x2 = c) equals -15.

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