Multiple choice

If m is a positive integer and r is the only value, which satisfies the quadratic equation y2 + my = -100, then the sum of m and r is

  1. -20

  2. -10

  3. 0

  4. 10

  5. 20
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D Correct answer
Explanation

y^2 + my + 100 = 0. For a unique root, the discriminant must be zero: m^2 - 4(1)(100) = 0, so m^2 = 400, m = 20 (since m is positive). The equation is y^2 + 20y + 100 = 0, which is (y+10)^2 = 0, so r = -10. m+r = 20 + (-10) = 10.

AI explanation

Rewrite the equation as the standard quadratic y^2 + my + 100 = 0. For this equation to have exactly one value of y that satisfies it, the discriminant (m^2 - 400) must equal zero, meaning m^2 = 400. Since m is a positive integer, m = 20, and substituting this back gives the single root r = -10. Therefore, the sum of m and r is 20 + (-10) = 10.

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