Correct Option: A
According to question ,
On Comparing x2 - 2( 1 + 3k )x + 7 ( 3 + 2k ) = 0 with ax2 + bx + c = 0, we get
a = 1, b = - 2 ( 1 + 3k ), c = 7( 3 + 2k )
For equal roots D = b2 - 4ac = 0
∴ 4( 1 + 3k )2 - 4 x 1 x 7( 3 + 2k ) = 0
⇒ 4( 1 + 9k2 + 6k ) - 84 - 56k = 0
⇒ 4 + 36k2 + 24k - 56k - 84 = 0
⇒ 36k2 - 32k - 80 = 0
⇒ 9k2 - 8k - 20 = 0
By shridharachary method ,
Here , A = 9 , B = -8 , C = -20
| k = | 8 ± √64 - 4(9) ( - 20 ) |
| 2 x 9 |
| k = | 8 ± √784 | = | 8 ± 28 |
| 18 | 18 |
Taking +ve and -ve sign respectively , we get
| k = | 36 | , | - 20 | = 2, | - 10 |
| 18 | 18 | 9 |
