Multiple choice

Two numbers p and q are such that the quadratic equation px2 + 3x + 2q = 0 has -6 as the sum and the product of the roots. What is the value of (p - q)?

  1. -1

  2. 1

  3. 2

  4. 3
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C Correct answer
Explanation

For px^2 + 3x + 2q = 0, sum of roots = -3/p = -6, so p = 0.5. Product of roots = 2q/p = -6, so 2q/0.5 = -6, 4q = -6, q = -1.5. Then p - q = 0.5 - (-1.5) = 2.

AI explanation

Using the sum and product formulas for the roots of px^2 + 3x + 2q = 0, we have -3/p = -6 and 2q/p = -6. From the first equation, multiplying both sides by p gives -3 = -6p, so p equals 1/2. Substituting p into the second equation gives 2q / (1/2) = -6, which simplifies to 4q = -6, or q equals -3/2. Subtracting q from p gives (1/2) - (-3/2), resulting in 2.

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