Multiple choice

If the sum as well as the product of the roots of the equation px2 - 6x + q = 0 is 6, then what is (p + q) equal to?

  1. 8

  2. 7

  3. 6

  4. 5
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B Correct answer
Explanation

For px^2 - 6x + q = 0, sum of roots = 6/p = 6, so p = 1. Product of roots = q/p = q/1 = 6, so q = 6. p + q = 1 + 6 = 7.

AI explanation

Using the relationships between roots and coefficients for the equation px2 - 6x + q = 0, the sum of the roots equals 6 divided by p and the product equals q divided by p. Because both the sum and the product equal 6, we set 6 divided by p equal to 6, which gives p equals 1. Substituting p equals 1 into the product formula, q divided by 1 equals 6, meaning q equals 6. Adding these coefficients together gives the final result of p plus q equals 7.

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