Multiple choice

If p and q are negative integers of the quadratic equation py2 + qy + r, having equal roots, then which of the following is definitely true?

  1. pqr > 0

  2. p + q + r < 0

  3. p + q - r < 0

  4. p + q + r > 0

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For py^2 + qy + r = 0 to have equal roots, the discriminant D = q^2 - 4pr = 0, so q^2 = 4pr. Since p and q are negative integers, q^2 is positive, so 4pr must be positive. Since p is negative, r must also be negative. If p, q, r are all negative, then p+q+r must be less than 0.

AI explanation

For the quadratic equation py^2 + qy + r = 0 to have equal roots, its discriminant (q^2 - 4pr) must be zero, meaning q^2 = 4pr. Since p and q are given as negative integers, q^2 is positive, which forces 4pr to be positive and thus r must also be negative. Because p, q and r are all negative, their sum p + q + r must be less than zero.

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