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Let "n" be a natural no. and let "a" be a real no. The no. of zeroes of x raised to 2n + 1 - ( 2n + 1) x + a = 0 in the interval of [ -1 , 1] is A) 2 if a>0 B) 2 if a<0 C) at most one for every value of a D) at least 3 for every value of a
The answer should be (c) In the question, x is raised to a power, and the only possible way to get 0 is when x is equal to 0. If suppose, x is not zero, and the power is any number, the output will not be zero, exponential functions are never zero. Now, since the zero exists when x=0, a can take up any value and the result will still be 0. Thus, the function can have at most one zero for every value of a.
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