Multiple choice

The number of real roots of equation 3x10 + 7x6 + 5x4 + 2x2 + 1 = 0 is

  1. three

  2. four

  3. six

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since all terms are even powers of x (x^10, x^6, x^4, x^2) with positive coefficients, 3x^10 + 7x^6 + 5x^4 + 2x^2 + 1 is always >= 1 for any real x. Therefore, there are no real roots.

AI explanation

Consider the nature of the terms in the polynomial equation 3x^10 + 7x^6 + 5x^4 + 2x^2 + 1 = 0. Because all coefficients are positive and all powers of x are even, the result of evaluating the left side for any real number will always be strictly positive. Since the sum of positive real numbers cannot equal zero, the equation cannot have any real roots. The number of real roots is zero, which falls under None of these.

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