If $(x + 1)$ and $(x - 2)$ are the factors of the expression $(2 x^{3} - p x^{2} + x + q)$ , then the values of $p$ and $q$ are given by:

p = 5, q = 2

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p = 7, q = 8

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p = 7, q = 10

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p = 15, q = 12

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Solution

The correct option is D $p = 7, q = 10$
$f (x) = 2 x^{3} - p x^{2} + x + q$
$f (- 1) = - 2 - p - 1 + q = 0$ $o r$ p-q=-3...(1)f(x)=16-4p+2+q=0 $o r$ 4p-q=18...(2) $S o l v i n g (1) a n d (2) w e h a v e$ p=7, q=10$

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Similar questions

(2 x^{3} - p x^{2} + x + q)

If (x-p) and (x-q) are the factors of the expression $a x^{2} + b x + c$ , then the values of $a$ and $b$ are:

‘p’ and ‘q’ are the zeroes of the polynomial $a x^{2} + b x + c = 0$ .

(x-p) and (x-q) are the only factors of the expression $a x^{2} + b x + c$ ,

The values of $a$ and $b$ are:

(a) Subtract 4a − 7ab + 3b + 12 from 12a − 9ab + 5b − 3

(b) Subtract 3xy + 5yz − 7zx from 5xy − 2yz − 2zx + 10xyz

4 a - 7 a b + 3 b + 12

12 a - 9 a b + 5 b - 3

3 x y + 5 y z - 7 z x

5 x y - 2 y z - 2 z x + 10 x y z

4 p^{2} q - 3 p q + 5 p q^{2} - 8 p + 7 q - 10

18 - 3 p - 11 q + 5 p q - 2 p q^{2} + 5 p^{2} q

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