First slide

Theory of equations

Question

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

Easy

A

45
B

48
C

51
D

54

Solution

clearly f(2)=0 or f(3)=0 $\Rightarrow f (2) = 16 - 24 + 20 - 66 + b = 0 \Rightarrow$ so b=54

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