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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). Like 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) = a x2 + bx + c, 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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