The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where

1.	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. 37212. 5493. 3614. 427
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

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. 37212. 5493. 3614. 427

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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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. 37212. 5493. 3614. 427

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