Algebrahard · Past Paper
If x^2 + px + q and x^2 + mx + n have a common factor (x - a), then a is:
A(n-q) / (p-m)
B(q-n) / (m-p)
C(p-m) / (n-q)
D(m-p) / (q-n)
✓ Correct Answer: A — (n-q) / (p-m)
a^2+pa+q = 0 and a^2+ma+n = 0. Subtract: (p-m)a + (q-n) = 0 => a = (n-q)/(p-m).
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