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JIPMAT 2022

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Easy

Which of the following is the value of mm for which the polynomial x4+10x3+25x2+15x+mx^4 + 10x^3 + 25x^2 + 15x + m is exactly divisible by x+7x+7?

Correct Option: 1
If polynomial is divisible by (x+7)(x + 7), then x=−7x = -7 should be a root. [Because x+7=0]x+7=0]
Substituting x=−7x = -7: \newline (−7)4+10(−7)3+25(−7)2+15(−7)+m(-7)^4 + 10(-7)^3 + 25(-7)^2 + 15(-7) + m \newline =2401−3430+1225−105+m= 2401 - 3430 + 1225 - 105 + m \newline =91+m= 91 + m
For polynomial to be exactly divisible by (x+7)(x + 7), this sum should be zero: \newline 91+m=091 + m = 0 \newline m=−91m = -91
Therefore, m=−91m = -91

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