If the equations $(a^{2} + b^{2}) x^{2} - 2 (a c + b d) x + c^{2} + d^{2} = 0$ has equal roots, then

(a) ab = cd
(b) ad = bc
(c) $a d = \sqrt{b c}$
(d) $a b = \sqrt{c d}$

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Solution

The given quadric equation is , and roots are equal.

Here,

As we know that

Putting the value of

The given equation will have equal roots, if

Thus, the correct answer is

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