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
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