Multiple choice

If one of the roots of the equation x2 – 13x + 2n + 5 = 0 is three more than the other, then what is the value of n?

  1. 17.5

  2. 18.5

  3. 19.5

  4. None of these

  5. Cannot be determined
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A Correct answer
Explanation

Let roots be a and a+3. Sum of roots = 2a + 3 = 13, so 2a = 10, a = 5. Roots are 5 and 8. Product of roots = 5 * 8 = 40. From equation, product = 2n + 5. 40 = 2n + 5 => 35 = 2n => n = 17.5.

AI explanation

Let the roots of the quadratic equation be p and p + 3. Using Vieta's formulas, the sum of the roots is p + (p + 3) = 13, which gives 2p + 3 = 13 and p = 5. The roots are 5 and 8. The product of the roots is 5 * 8 = 40. From the equation, the product of the roots equals 2n + 5, so 2n + 5 = 40. Solving for n gives 2n = 35 and n = 17.5. The value of n is 17.5.

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