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Question

If
Δ(x)=∣ ∣ ∣x25x+32x533x2+x+46x+197x26x+914x621∣ ∣ ∣=ax3+bx2+cx+d then

A
a=0
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B
b=0
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C
c=0
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D
d=144
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Solution

The correct options are
A a=0
B b=0
C c=0
D d=144
Differentiate both the sides with respect to x
Δ(x)=∣ ∣2x52x536x+16x+1914x614x621∣ ∣+∣ ∣ ∣x25x+3233x2+x+4697x26x+91421∣ ∣ ∣
=0+0=0
Δ(x) is a constant
Thus, a=0,b=0 & c=0
For value of d , putting x=0
Δ(0)=∣ ∣ ∣025.0+32.0533.02+0+46.0+197.026.0+914.0621∣ ∣ ∣=a.03+b.02+c.0+dd=144

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