# If both (x – 2) and (x – 1/2) are factors of px^2 + 5x + q, show that p = q.

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If both (x – 2) and (x – 1/2) are factors of px2 + 5x + q, show that p = q.

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Let f(x) = px2 + 5x + q, if (x – 2) is the factor of f(x)

from (1) and (2)

⇒ 4p + 10 + q = p + 10 + 4q

⇒ 4p + q = p + 4q

⇒ 4p – p = 4q – q

⇒ 3p = 3q

⇒ p = q