If x² - px + 72 has factors differing by 1, then p equals?
- 17
- 18
- 19
- None of these
Explanation
If x² - px + 72 has factors differing by 1, then p = ±17
Solution in older version:
Let the two factors be m and m+1.
Then,
x² - px + 72 = (x - m)(x - (m+1))
= (x - m)(x - m - 1)
= x² - (2m + 1)x + m(m+1)
Compare with x² - px + 72:
1. m(m+1) = 72
2. p = 2m + 1
Solve m(m+1) = 72:
m² + m - 72 = 0
(m + 9)(m - 8) = 0
So m = 8 or m = -9
Case 1: m = 8
Factors are 8 and 9
p = 2_8 + 1 = 17
Case 2: m = -9
Factors are -9 and -8
p = 2_(-9) + 1 = -17
Last verified on 24-05-2026
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