First slide

Theory of expressions

Question

The value of k , so that $x^{4} - 3 x^{3} + 5 x^{2} - 33 x + k$ is divisible by $x^{2} - 5 x + 6$ is

Easy

A

45
B

48
C

51
D

54

Solution

Let the given equation is $f (x) = x^{4} - 3 x^{3} + 5 x^{2} - 33 x + k = 0$ ….. ( 1 )
Eq. ( 1 ) is divisible by $x^{2} - 5 x + 6$

The factors of given $x^{2} - 5 x + 6$ are

$\Rightarrow (x - 2) (x - 3) = 0$

$\Rightarrow x = 2, x = 3$

Put $x = 2$ ( or ) $x = 3$ in Eq. ( 1 )

$\Rightarrow f (2) = 2^{4} - 3 {(2)}^{3} + 5 {(2)}^{2} - 33 (2) + k = 0$

$\Rightarrow k = 54$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App