Multiple choice

If p and q are the roots of the equation x2 - 15x + r = 0 and p - q = 1, then what is the value of r?

  1. 55

  2. 56

  3. 60

  4. 64
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B Correct answer
Explanation

Roots p, q. p+q = 15, p-q = 1. Adding: 2p = 16 => p = 8. Subtracting: 2q = 14 => q = 7. r = p*q = 8 * 7 = 56.

AI explanation

The sum of the roots gives p + q = 15, and we are given the difference p - q = 1. Adding these two equations yields 2p = 16, so p = 8, and subsequently subtracting the difference equation gives q = 7. The value of r is the product of the roots, so r = p multiplied by q, which equals 8 times 7, giving r = 56.

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