Find k for which quadratic equation (k – 12) x2 + 2(k – 12)x + 2

1.	Find k for which quadratic equation (k – 12) x2 + 2(k – 12)x + 2 = 0 has equal and real roots.
Answer» Given (k – 12)x² + 2(k – 12)x + 2 = 0 Comparing it with quadratic equation ax² + bx + c = 0 a = (k – 12),b = 2(k – 12), c = 2 Discriminant (D) = b² – 4ac = 4(k – 12)² – 4 × (k – 12) × 2 = 4(k – 12) [k – 12 – 2] = 4(k – 12)(k – 14) Given equation will have real and equal roots, if discriminant = 0. D = 0 ⇒ 4(k – 12)(k – 14) =0 ⇒ k – 12 = 0 or k – 14 = 0 ⇒ k = 12 or k = 14

Find k for which quadratic equation (k – 12) x2 + 2(k – 12)x + 2 = 0 has equal and real roots.

Answer»

Given

(k – 12)x² + 2(k – 12)x + 2 = 0

Comparing it with quadratic equation

ax² + bx + c = 0

a = (k – 12),b = 2(k – 12), c = 2

Discriminant (D) = b² – 4ac

= 4(k – 12)² – 4 × (k – 12) × 2

= 4(k – 12) [k – 12 – 2]

= 4(k – 12)(k – 14)

Given equation will have real and equal roots, if discriminant = 0.

D = 0

⇒ 4(k – 12)(k – 14) =0

⇒ k – 12 = 0 or k – 14 = 0

⇒ k = 12 or k = 14