When x3+5 x2-k x+8 is divided by (x-3) the remainder is k. Find the value of k.

Question

When x3+5 x2-k x+8 is divided by (x-3) the remainder is k. Find the value of k. (A) k< 18 (B) k >15 (C) 21 >k >19 (D) k ≥ 20

Tardigrade Admin · Accepted Answer

f(x)=x3+5 x2-k x+8 By remainder theorem, when f(x) is divided by (x-3) the remainder is f(3) =(3)3+5(3)2-k(3)+8 =27+45-3 k+8=80-3 k According to the given information, 80-3 k=k ⇒ 4 k=80 text or k=20

Q. When $x^{3} + 5 x^{2} - k x + 8$ is divided by $(x - 3)$ the remainder is $k$ . Find the value of $k$ .

$k < 18$

$k > 15$

$21 > k > 19$

$k \geq 20$

$f (x) = x^{3} + 5 x^{2} - k x + 8$
By remainder theorem, when $f (x)$ is divided by $(x - 3)$ the remainder is $f (3)$
$= (3)^{3} + 5 (3)^{2} - k (3) + 8$
$= 27 + 45 - 3 k + 8 = 80 - 3 k$
According to the given information,
$80 - 3 k = k$
$\Rightarrow 4 k = 80 or k = 20$

Q. When x3+5x2−kx+8 is divided by (x−3) the remainder is k. Find the value of k.

k<18

k>15

21>k>19

k≥20