1950 AHSME Problems/Problem 15

Problem

The real roots of $x^2+4$ are:

$\textbf{(A)}\ (x^{2}+2)(x^{2}+2)\qquad\textbf{(B)}\ (x^{2}+2)(x^{2}-2)\qquad\textbf{(C)}\ x^{2}(x^{2}+4)\qquad\\ \textbf{(D)}\ (x^{2}-2x+2)(x^{2}+2x+2)\qquad\textbf{(E)}\ \text{Non-existent}$

Solution

This looks similar to a difference of squares, so we can write it as $(x+2i)(x-2i).$ Neither of these factors are real.

Also, looking at the answer choices, there is no way multiplying two polynomials of degree $2$ will result in a polynomial of degree $2$ as well. Therefore the real factors are $\boxed{\mathrm{(E)}\text{ Non-existent.}}$

1950 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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1950 AHSME Problems/Problem 15

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