Q8 of 168 Page 7

For what values of k, does the following quadratic equation has equal roots.
9x² + 8kx + 16 = 0

Since roots are equal

∴ d=0 (1)

9x² + 8kx + 16 = 0

d = b² – 4ac

d = (8k)² – 4 (9) (16)

From (1), d = 0

∴ Equation will be:

0 = 64k² – 576

k² = 9

k = ±√9

k = 3, –3

∴ values of k are –3, 3 .

Find the value of k for which the quadratic equation

4x² — 2 (k + 1) x + (k + 4) = 0 has equal roots.

Find the value of k, so that the quadratic equation

(k + 1) x² – 2 (k — 1) x + 1 = 0 has equal roots.

(k + 4)x² + (k + 1)x + 1 = 0

k²x² — 2(2k — 1)x + 4 = 0

For what values of k, does the following quadratic equation has equal roots.9x2 + 8kx + 16 = 0