Question

f (x + a) is a factor of two polynomials x2 +p x +q and x2 + mx + n then prove that a = n - q / m - p .​

Answer 1

Answer:

(x + a) is a factor of x + px + q

:. (-a)2 + p(-a) + q =0

= a2 - ap + q = 0 ...(1)

(x + a) is a factor of x + mx + n

(-a)2 + m (-a) + n = 0

= a2 - am + n = 0...(ii)

From (i) and (ii),

-ap + am + q - n = 0

a(m - p) = n - q

a=n-q/m-p

Explanation:

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