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 =

x + a = 0 ⇒ x = -a. Since, (x + a) is factor of f(x) and g(x). ∴ f(-a) = g(-a) ⇒ (-a) 2 + p(-a) + q = (-a) 2 + m(-a) + n ⇒ a 2 - pa + q = a 2 - ma + n ⇒ a 2 - a 2 - pa + ma = n - q ⇒ ma - pa = n - q ⇒ a(m - p) = n - q ⇒ a = . Hence, proved that a = .

Mathematics

If x + a is a common factor of expressions f(x) = x² + px + q and g(x) = x² + mx + n; show that : a = $\dfrac{n - q}{m - p}$

Factorisation

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Answer

x + a = 0 ⇒ x = -a.

Since, (x + a) is factor of f(x) and g(x).

∴ f(-a) = g(-a)

⇒ (-a)² + p(-a) + q = (-a)² + m(-a) + n

⇒ a² - pa + q = a² - ma + n

⇒ a² - a² - pa + ma = n - q

⇒ ma - pa = n - q

⇒ a(m - p) = n - q

⇒ a = $\dfrac{n - q}{m - p}$ .

Hence, proved that a = $\dfrac{n - q}{m - p}$ .

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Mathematics

If x + a is a common factor of expressions f(x) = x² + px + q and g(x) = x² + mx + n; show that : a = $\dfrac{n - q}{m - p}$

Factorisation

Answer

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