Correct Answer - Option 3 : -7/3, -9/2

**Given:**

6x2 + 41 x + 63 = 0

**Calculation:**

Using middle term factorisation:

6x^{2} + 14x + 27x + 63 = 0 ∵ (14 × 27 = 6 × 63 = 378 & 14 + 27 = 41)

2x ( 3x + 7 ) + 9 ( 3x + 7 ) = 0

( 2x + 9 ) ( 3x + 7 ) = 0

So, the roots are:

2x + 9 = 0

x = -9/2

3x + 7 = 0

x = -7/3

**∴ The value of roots for the quadratic equation 6x2 + 41 x + 63 = 0 is -9/2 and -7/3**