Given that k is not equal to -1.. (C1 Maths Q)

Please show me how to answer the following question:

Given that k is not equal to -1, show that the quadratic equation
(k + 1)x² + 2kx + (k - 1) = 0
has two distinct real roots.

Thanks in advance

Use the discriminant of quadratic equations for this question. For a quadratic equation to have two distinct real roots, b^2 - 4ac must be greater than 0.

b^2 - 4ac = (2k)^2 - 4(k+1)(k-1)

Simplify and evaluate this expression:
4k^2 - 4(k^2 - 1) = 4k^2 - 4k^2 + 4 = 4.

Since the discriminant, b^2 - 4ac = 4 is greater than 0, the quadratic equation in your question will always have two distinct real roots.

and as discriminant is a square so roots shall be rational as well
also we can factor it as
(k + 1)x² + 2kx + (k - 1)
= (k+1) x^2 + x(k+1) + x(k-1) + (k-1)
= (k+1) x(x+1) + (k-1)(x+1)
= (x+1)(kx + x + k - 1)
so roots are real( k is real)

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