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The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?
1. 3721
2. 549
3. 361
4. 427

1 Answer

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Best answer
Correct Answer - Option 2 : 549

Calculation:

Sum of roots = – b

4a + 3a = – b

⇒ 7a = – b

⇒ 49a2 = b2

Product of roots = c

4a × 3a = c

⇒ 12a2 = c

b2 + c = 49a2 + 12a2

⇒ 61a2

⇒ 61 × 16 = 976

⇒ 61 × 9 = 549

∴ Possible value of b2 + c is 549

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