Multiple choice

The equation px2 + qx + r = 0 (where p, q and r, all are positive) has distinct real roots a and b. Which one of the following is correct?

  1. a > 0, b > 0

  2. a < 0, b < 0

  3. a > 0, b < 0

  4. a 0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The product of the roots is r/p, which is positive, so the roots have the same sign. Their sum is -q/p, which is negative, so both distinct real roots must be negative.

AI explanation

Given the equation px^2 + qx + r = 0 with positive coefficients, the sum of the roots is -q/p and the product of the roots is r/p. Because p, q, and r are all positive, the product r/p is positive, meaning both roots have the same sign. Since the sum of the roots is -q/p, it must be a negative value, meaning the sum of the two same-signed numbers is negative. Therefore, both roots must be strictly negative, confirming that a < 0 and b < 0.

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