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Maths-

General

Easy

Question

If $capital delta$ (x) = $open vertical bar table row cell e to the power of x end cell cell s i n invisible function application 2 x end cell cell t a n invisible function application x squared end cell row cell invisible function application left parenthesis 1 plus x right parenthesis end cell cell c o s invisible function application x end cell cell s i n invisible function application x end cell row cell c o s invisible function application x squared end cell cell e to the power of x minus 1 end cell cell s i n invisible function application x squared end cell end table close vertical bar$ = A + Bx + Cx², then B is equal to

0
1
2
None of these

The correct answer is: 0

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If ax³ + bx² + cx + d = $open vertical bar table row cell x to the power of 2 end exponent end cell cell left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 2 right parenthesis to the power of 2 end exponent end cell row cell left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 2 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 3 right parenthesis to the power of 2 end exponent end cell row cell left parenthesis x minus 2 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 3 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 4 right parenthesis to the power of 2 end exponent end cell end table close vertical bar$ , then

If ax³ + bx² + cx + d = $open vertical bar table row cell x to the power of 2 end exponent end cell cell left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 2 right parenthesis to the power of 2 end exponent end cell row cell left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 2 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 3 right parenthesis to the power of 2 end exponent end cell row cell left parenthesis x minus 2 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 3 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x minus 4 right parenthesis to the power of 2 end exponent end cell end table close vertical bar$ , then

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