Two numbers \( a \) and \( b \) are chosen at random from the set \...

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Two numbers \( a \) and \( b \) are chosen at random from the set \( \{1,2,3, \ldots, 9\} \) with replacement. The probability that the equation
\[
x^{2}+\sqrt{2}(a-b) x+b^{2}=0
\]
has
Column 1
Column 2
(a) real roots
(p) \( 34 / 81 \)
(b) equal roots
(q) 0
(c) imaginary roots
(r) \( 2 / 81 \)
(d) positive roots
(s) \( 5 / 81 \)
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