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Question

If x2−3x+2 is factor of x4−ax2+b, then

A
a=5
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B
b=4
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C
all roots of x4ax2+b=0 are real and distinct
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D
a=4,b=5
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Solution

The correct options are
A a=5
B b=4
C all roots of x4ax2+b=0 are real and distinct
Let f(x)=x4ax2+b
As x23x+2=(x2)(x1) is a factor
f(2)=24a22+b=0164a+b=04ab=16 ...(1)
f(1)=14a12+b=0ab=1 ...(2)
Solving (1) and (2),we get
a=5,b=4
Hence, options 'A' and 'B' are correct.

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