The set S has elements of the form 2n, with n taking on all natural number values. Let m be any element of S. If p is the number of real roots of the equation xm+ 1 - x = 0, how many different values are possible for p?Correct answer is '1'. Can you explain this answer?

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CAT Question > The set S has elements of the form 2n, with n...

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The set S has elements of the form 2ⁿ, with n taking on all natural number values. Let m be any element of S. If p is the number of real roots of the equation x^{m + 1} - x = 0, how many different values are possible for p?

Correct answer is '1'. Can you explain this answer?

Verified Answer

The set S has elements of the form 2n, with n taking on all natural nu...

Let m - 2ⁿ for some natural number n.
Consider the equation,

x^m+1- x = 0

x(x^m - 1) = 0

x = 0 or x^m = 1

m is even,

the possible real roots of the equation are, -1, 0 and 1.
Since p = 3 for all n and m, there is only one possible value of p. Answer: 1

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The set S has elements of the form 2n, with n taking on all natural number values. Let m be any element of S. If p is the number of real roots of the equation xm+ 1 - x = 0, how many different values are possible for p?Correct answer is '1'. Can you explain this answer?

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