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If x= 2 + 3 + 6 is a root of x^4+a x^3+b x^2+c x+d=0 where a, b, c, d are integers, what is the value of | a + b + c + d | ?

Correct answer

93

Step-by-step solution

x= 2 + 3 + 6 root of equation : x^4+a x^3+b x^2+c x+d=0 ; a, b, c, d Z Now, aligned & (x- 2 )^2=( 3 + 6 )^2 x^2-2 2 x+2=9+6 2 & x^2-7=2 2 (3+x) aligned (On squaring both sides) array ll & x ^4-14 x ^2+49=8 ( x ^2+6 x +9 ) & x ^4-22 x ^2-48 x -23=0 & a=0, b=-22, c=-48 and d=-23 & |a+b+c+d|=93 array

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