Question

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

Answer 1

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Answer 2

$k=\dfrac{q-m}{p-l}$

Step-by-step explanation:

Given,

(x + k) is a common factor of $(x^2+px+q)$ and $(x^2 + lx + m)$.

To find, the value of k = ?

∴ x + k = 0

⇒ x = - k

$(-k)^2+p(-k)+q=0$

$k^2-pk+q=0$           .......(1)

and

$(-k)^2 + (-k)l + m)=0$

$k^2 -kl + m=0$        .......(2)

Subtracting (1) from (2), we get

$(k^2 -kl + m)-(k^2-pk+q)=0$

⇒ $k^2 -kl + m-k^2+pk-q=0$

⇒ $-kl + m+pk-q=0$

⇒ $k(p-l)=q-m$

⇒  $k=\dfrac{q-m}{p-l}$

Hence, $k=\dfrac{q-m}{p-l}$