If x² - px + 48 has factors differing by 2, then p equals?
- 12
- 13
- 14
- None of these
Explanation
Let the two factors be (x - a) and (x - b)
Then:
1. (x - a)(x - b) = x^2 - (a + b)x + ab
2. Compare with x^2 - px + 48:
ab = 48
a + b = p
3. Given: a - b = 2 => a = b + 2
Substitute:
(b + 2)b = 48
b^2 + 2b - 48 = 0
(b + 8)(b - 6) = 0
So b = 6 or b = -8
If b = 6, then a = 8, p = a + b = 14
If b = -8, then a = -6, p = a + b = -14
Last verified on 15-05-2026
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