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). 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 $x^{2}$ + bx + c, 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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