Discussion

Explanation:

One of the roots of the given equation = 27-5 × 7+57+5 = √7+√5

Since, a and c are rational, c/a i.e., product of the roots will also be rational.

If x is the other root of this equation, then product of roots, c/a = (√7 + √5) × x

⇒ x = c/a7+5 = c2a7-5

Now, Sum of the roots = (√7 + √5) + c2a7-5-ba

⇒ -2b = 2a(√7 + √5) + c(√7 - √5)

Hence, option (d).

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