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Bunuel
Which of the following could equal zero for some value of x?

I. \(3x^2 − 12\)

II. \(x^2 + x^4 + 1\)

III. \(x^2 + 7x + 6\)

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

If you want to save time on such questions..
x could be ANYTHING - fraction, integers, negative or positive

I. \(3x^2 − 12\)..There has to be a value of x, rather 2 values - positive and negative both, that will make equation 0. No need to check values...YES

II. \(x^2 + x^4 + 1\)... Both x^2 and x^4 will be positive except when x=0. Still the least value of term will be 1 at x=0....NO

III. \(x^2 + 7x + 6\) ..Again, there has to be a NEGATIVE value of x, that will make equation 0. Since it is a quadratic equation, that is equation with x^2, there will be two values/roots. No need to check values...YES

I and III

D
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ans d
as only 1 and 3 has odd power of x which could possibly lead to negative values.
option 2 will always give positive values which can never lead the addition to zero

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