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Standard XII

Mathematics

Definition of Functions

When a polyno...

Question

When a polynomial $p (x)$ is divided by $x - 2,$ the remainder is $7.$ When $p (x)$ is divided by $x - 3,$ the remainder is $9.$ If $r (x)$ is the remainder when $p (x)$ is divided by $(x - 2) (x - 3),$ then the value of $r (- 1)$ is

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Solution

The correct option is B $1$
Given that $p (2) = 7 & p (3) = 9$
Let $p (x) = (x - 2) (x - 3) g (x) + r (x)$
Since the degree of the remainder is always less than the degree of divisor, we get
$r (x) = A x + B$

$\Rightarrow 2 A + B = 7$ and $3 A + B = 9$
$\Rightarrow A = 2$ and $B = 3$
$∴ r (x) = 2 x + 3$
$\Rightarrow r (- 1) = 1$

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When a polynomial p(x) is divided by x−2, the remainder is 7. When p(x) is divided by x−3, the remainder is 9. If r(x) is the remainder when p(x) is divided by (x−2)(x−3), then the value of r(−1) is

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