Question

For what values of k will the equation

$x^{2} - 2(1 + 3k)x + 7(3 + 2k) = 0$ have equal roots

• A. 1, –10/9
• B. 2, –10/9
• C. 3, –10/9
• D. 4, –10/9

Answer 1

Answer: (B)

2, –10/9

Answer 2

Since roots are equal then $\lbrack - 2(1 + 3k)\rbrack^{2} = 4.1.7(3 + 2k)$

⇒ $1 + 9k^{2} + 6k = 21 + 14k$

⇒ $9k^{2} - 8k - 20 = 0$

Solving, we get $k = 2, - 10/9$