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Question

# If ‘p’ and ‘q’ are the zeroes of the polynomial P(x) = x2 + ax + b =0, then P(x) can be written as:

A

(x + p) (x + q)

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B

(x – p) (x – q)

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C

(x +p ) ( x – q)

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D

(x – p) ( x + q)

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Solution

## The correct option is B (x – p) (x – q) A polynomial P(x) of any degree can be written as product of all the factors of P(x). If we know that ‘a’ and ‘b’ are the zeroes of P(x) then P(x) = (x- a) (x – b). In the above question, it is given that ‘p’ and ‘q’ are the zeroes of P(x) = x2 + ax + b, it means (x- p) and (x – q) are the factors of the equation, P(x) = ax2 + bx + c. Hence, P(x) = (x – p) (x – q).

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