If x² - px + 35 has factors differing by 2, then p equals?
- 12
- 13
- 14
- None of these
Explanation
Let the roots be r and r + 2, since they differ by 2.
For x² - px + 35 = 0:
Product of roots = r(r + 2) = 35
Sum of roots = r + (r + 2) = 2r + 2 = p
Solve r(r + 2) = 35:
r² + 2r - 35 = 0
(r + 7)(r - 5) = 0
So r = 5 or r = -7
Case 1: r = 5 → roots are 5 and 7 → p = 5 + 7 = 12
Case 2: r = -7 → roots are -7 and -5 → p = -7 + (-5) = -12
So p = 12 or -12
Last verified on 13-05-2026
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