In order to have

\(3a^2 + 5b^2 = 0\)

a^2 must be equal to zero

which means that a=0

b^2 as well

so both a and b are zero

In quantity A , having a and b = 0, we will have 0-0=0

B is zero

The answer is C

\(3a^2 + 5b^2 = 0\)

\(3a^2 = -5b^2\)

\(a = \sqrt{\frac{-5b^2}{3}}\)

\(a = \sqrt{\frac{5}{3}}bi\)

We are getting Imaginary numbers here! Which is never asked on GRE

Therefore, \(3a^2 + 5b^2\) can only be equal to zero if both \(a\) and \(b\) are zero

Col. A: \(5(0) - 3(0) = 0\)
Col. B: \(0\)

Hence, option C

if a=0 and b=0
the two are equal


Answer - C

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