Question

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Answer 1

Step-by-step explanation:

 For unequal and real roots, discriminant must be greater than 0.       In standard eq. discriminant = b^2 - 4ac.

Here,

 a = 1     , b = - 2(k + 1)   ; c = k^2

 Conditions:

⇒ [-2(k + 1)]^2 - 4(1)(k^2) > 0

⇒ 4(k + 1)^2 - 4k^2 > 0

⇒ 4[ (k + 1)^2 - k^2] > 0

⇒ (k + 1)^2 - k^2 > 0

⇒ k^2 + 1 + 2k - k^2 > 0

⇒ 1 + 2k > 0

⇒ k > - 1/2

       Hence, for any value greater than - 1/2, equal will give real and unequal roots.