Q2 of 227 Page 110

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

x2 + 2k (x – 2) + 5 = 0


⇒ x2 + 2kx – 4k + 5 = 0






∴


⇒ 4k2 + 16k – 20 =0


Divide by 4


⇒ k2 + 4k – 5 = 0


⇒ k2 + 5k – k – 5 = 0


⇒ k(k + 5) – (k + 5) =0


⇒ (k + 5)(k – 1) = 0


k + 5 = 0 or k – 1 = 0


k = –5 or k = 1


∴ k = –5 and k = 1


More from this chapter

All 227 →
2

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

2x2 – 10x + k = 0

 2

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

12x2 + 4kx + 3 = 0

 2

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

 3

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