Find the value(s) of k so that the quadratic equation x2 – 4kx + k = 0 has equal roots. (CBSE 2012)

For a quadratic equation, ax2 + bx + c = 0, D = b2 – 4ac If D = 0, roots are real and equal ⇒ D = 16k2 – 4k = 0 ⇒ 4k(4k – 1) = 0 ⇒ k = 0, 1/4

Q8 of 82 Page 4

Find the value(s) of k so that the quadratic equation x² – 4kx + k = 0 has equal roots. (CBSE 2012)

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

D = b² – 4ac

If D = 0, roots are real and equal

⇒ D = 16k² – 4k = 0

⇒ 4k(4k – 1) = 0

⇒ k = 0, 1/4

Find the value of m so that the quadratic equation mx (x – 7) + 49 = 0 has two equal roots. (CBSE 2011)

Find the value of p so that the quadratic equation px (x- 3) + 9 = 0 has two equal roots. (CBSE 2011)

Find the value(s) of k so that the quadratic equation 3x² – 2kx + 12 = 0 has equal roots? (CBSE 2012)

For what value of k does the quadratic equation

(k – 12) x² + 2(k – 12) x +2 = 0 have equal roots? (CBSE 2013)