Multiple choice

If the equation y2 - 6y + r = 0 has both its roots as positive integers, how many possible values can r take?

  1. 1

  2. 2

  3. 3

  4. 4

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

Roots are positive integers. Sum = 6, Product = r. Possible pairs (sum=6): (1,5), (2,4), (3,3). Products: 1*5=5, 2*4=8, 3*3=9. There are 3 possible values for r.

AI explanation

For the equation y2 - 6y + r = 0, the sum of the roots is 6 and the product is r. If both roots are positive integers, the only pairs adding up to 6 are (1, 5), (2, 4) and (3, 3). The corresponding products are 5, 8 and 9, meaning r can be any of these three distinct values.

Keep practicing — related questions