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Maximum number of real solution does the equation x^7+ax^5+bx^3+cx-d=0(a,b,c,d>0)
Dear Suraj f’(x) = 7x^6 + 5ax^4 + 3b x^2 +c this is always postive hence this is incresing function. hence it will cut x axis only one time. hence number of real roots = 1
Dear student Here is the correct explanation f’(x) = 7x^6 + 5ax^4 + 3b x^2 +cThis is greater than zero Because a, b , c , d > 0 f'(x) > 0=> This indictes it is monotonically increasing Lim (x->-inf. ) f(x) = -infinity Lim (x->inf. ) f(x) = infinity So, it has maximum real roots = 1 Complex real roots = 7-1 =6
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