#### Question

If x + a is a common factor of expressions f(x) = x^{2} + px + q and g(x) = x^{2} + mx + n;

show that : `a=(n-q)/(m-p)`

#### Solution

`f(x)=x^2+px+q`

it is given that (x+a) is a factor of f(x)

∴ f(-a)=0

⇒`(-a)^2+p(-a)+q=0 `

⇒ `a^2-pa+q=0 `

⇒ `a^2=pa-q ` ........(1)

`g(x)=x^2+mx+n `

it is given thhat (x+a) is a factor of g (x).

∴ `g(-a)=0 `

⇒ `(-a)^2+m(-a)+n=0 `

⇒ `a^2-ma+n=0 `

⇒ `a^2=ma-n` ........(2)

from (1) and (2), we get,

`pa-q=ma-n `

`n-q=a(m-p) `

`a=(n-q)/(m-p)`

Hence, proved.

Is there an error in this question or solution?

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If X + a is a Common Factor of Expressions F(X) = X2 + Px + Q and G(X) = X2 + Mx + N; Show that : A=(N-q)/(M-p) Concept: Factor Theorem.

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