Prove that the roots of the equation x2 + (k − 2)x – 2k = 0 are real and distinct for all real values of k.

Step-by-step explanation:

Use the discriminate of the quadratic equation.

a = 1

b = k - 2

c = - 2k

Discriminate (D)  = sqrt(b^2 - 4*a*c)

D = sqrt( (k - 2)^2 - 4(1)(-2k) )

D = sqrt( k^2 -4k + 4 + 8k)

D = sqrt(k^2 +4k + 4)

D = sqrt(k + 2)^2

D = (k+2)

The domain of k can be any real number -- nothing is excluded.

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