Given that the quadratic equation (k^2-1) x^2-2kx+3k+1=0 has equal roots show that 3K^3-3K-1=0

Step-by-step explanation:

The roots are equal, so the discriminant equals 0.

b² - 4ac = 0

(2k) ² - 4 (k²-1) (3k+1) = 0

4k² - 4 (3k³ + k² - 3k - 1) = 0

k² - (3k³ + k² - 3k - 1) = 0

k² = 3k³ + k² - 3k - 1

0 = 3k³ - 3k - 1