If x² - px + 90 has factors differing by 9, then p equals?
- 23
- 22
- 21
- None of these
Explanation
Let the factors be (x - m) and (x - n)
Then:
m + n = p
m * n = 90
|m - n| = 9
Using (m - n)^2 = (m + n)^2 - 4mn:
9^2 = p^2 - 4*90
81 = p^2 - 360
p^2 = 441
p = ±21
Last verified on 25-05-2026
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