If (x + k) is a common factor of x2 + px + q and x2 + lx + m, then the

1.	If (x + k) is a common factor of x2 + px + q and x2 + lx + m, then the value of k is(a) \(\frac{P+q}{l+m}\)(b) \(\frac{P-l}{q-m}\)(c) \(\frac{q+m}{q+l}\)(d) \(\frac{q-m}{p-l}\)
Answer» (d) \(\frac{q-m}{p-l}\) Let f(x) = x² + p\(x\) + q g(x) = x² + l\(x\) + m. Since (x + k) is a common factor of f(x) and g(x), f(–k) = k² – pk + q = 0 g(–k) = k² – lk + m = 0 ⇒ k² – px + q = k² – lk + m ⇒ q – m = (p – l)k ⇒ k = \(\frac{q-m}{p-l}\)

If (x + k) is a common factor of x2 + px + q and x2 + lx + m, then the value of k is(a) \(\frac{P+q}{l+m}\)(b) \(\frac{P-l}{q-m}\)(c) \(\frac{q+m}{q+l}\)(d) \(\frac{q-m}{p-l}\)

Answer»

(d) \(\frac{q-m}{p-l}\)

Let f(x) = x² + p\(x\) + q

g(x) = x² + l\(x\) + m.

Since (x + k) is a common factor of

f(x) and g(x), f(–k) = k² – pk + q = 0

g(–k) = k² – lk + m = 0

⇒ k² – px + q = k² – lk + m

⇒ q – m = (p – l)k ⇒ k = \(\frac{q-m}{p-l}\)