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15-05-2020
Mathematics

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

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MathPhys MathPhys

15-05-2020

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

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