If `a ,b ,c ,d` are four consecutive terms of an increasing A.P., then the roots of the equation `(x-a)(x-c)+2(x-b)(x-d)=0` are a. non-real complex b. real and equal c. integers d. real and distinct

Explanation

To solve the problem, we need to analyze the given equation and determine the nature of its roots. The equation is:

\[ (x-a)(x-c) + 2(x-b)(x-d) = 0 \]

Given that \(a, b, c, d\) are four consecutive terms of an increasing arithmetic progression (A.P.), we can express them as:

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