Find the values of k for which the given quadratic equation has real and distinct roots:

(i)

(ii)

(iii)

For a quadratic equation, ax² + bx + c = 0,

D = b² – 4ac

If D > 0, roots are real and distinct

⇒ D = 4 – 4k

⇒ 4 – 4k > 0

⇒ k < 1

(ii)

For a quadratic equation, ax² + bx + c = 0,

D = b² – 4ac

If D > 0, roots are real and distinct

⇒ D = 36 – 4k

⇒ 36 – 4k > 0

⇒ k < 9

(iii)

For a quadratic equation, ax² + bx + c = 0,

D = b² – 4ac

If D > 0, roots are real and distinct

⇒ D = k² – 36

⇒ k² – 36 > 0

⇒ (k + 6)(k – 6) > 0

⇒ k < -6 or k > 6