If ‘p’ and ‘q’ are the zeroes of the polynomial P(x) = $x^{2}$ + ax + b =0, then P(x) can be written as:

(x + p) (x + q)

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(x – p) (x – q)

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(x +p ) ( x – q)

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(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) = $x^{2}$ + ax + b, it means (x- p) and (x – q) are the factors of the equation,
P(x) = a $x^{2}$ + bx + c.
Hence, P(x) = (x – p) (x – q).

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Similar questions

If ‘p’ and ‘q’ are the zeroes of the polynomial P(x) = $x^{2}$ + ax + b =0, then P(x) can be written as

If (x – p) and (x – q) are the factors of the polynomial P(x) = $x^{2}$ + ax + b =0, then P(x) can be written as:

Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x)=3x+1,x= $\frac{- 1}{3}$

(ii) p(x)=5x− $π$ ,x= $\frac{4}{5}$

(iii) p(x)= $x^{2}$ -1,x=1,−1

(iv) p(x)=(x+1)(x−2),x=−1,2

(v) p(x)= $x^{2}$ ,x=0

Verify whether the following are zeroes of the polynomial, indicated against them.

(i) (ii)

(iii) p(x) = x² − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2

(v) p(x) = x², x = 0 (vi) p(x) = lx + m

(vii) (viii)

Factorise the given expression:
$x y - p q + q y - p x$

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