Q2 of 227 Page 110

Find the values of k for which the roots are real and equal in each of the following equations
(k + 1) x² – 2 (k – 1) x + 1 = 0

(k + 1) x² – 2 (k – 1) x + 1 = 0

∴

⇒ 4k² – 8k + 4 – 4k – 4 = 0

⇒ 4k² – 12k = 0

Divide by 4

⇒ k² – 3k = 0

⇒ k(k – 3) = 0

⇒ k = 0 or k– 3 = 0

k = 0 or k = 3

∴ k = 0 and k = 3

Find the values of k for which the roots are real and equal in each of the following equations

12x² + 4kx + 3 = 0

Find the values of k for which the roots are real and equal in each of the following equations

x² + 2k (x – 2) + 5 = 0

Show that the roots of the equation x² + 2(a + b) x + 2 (a² + b²) = 0 are unreal.

Show that the roots of the equation 3p²x² – 2pqx + q² = 0 are not real.

Find the values of k for which the roots are real and equal in each of the following equations(k + 1) x2 – 2 (k – 1) x + 1 = 0