Discussion

Explanation:

Given quadratic equation is x2 + bx + c = 0

Sum of roots = -b

⇒ -b = 4a + 3a

⇒ -b = 7a

Product of the roots = c

⇒ c = 4a × 3a

⇒ c = 12a2

Now, b2 = 49a2 and c =12a2

Hence, b2 + c = 49a2 + 12a2

⇒ b2 + c = 61a2

Final answer must be a multiple of 61 & the multiple should be a perfect square.

Going through the options,

3721 = 61 × 61 (multiple is not a perfect square)

361 (not a multiple of 61)

427 = 61 × 7 (multiple is not a perfect square)

549 = 61 × 9 = 61 × 32

Thus, possible value of b2 + c = 549.

Hence, option (b).

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