Q7 of 168 Page 7

Find the value of k for which the quadratic equation

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

Since roots are equal


∴ d=0 ….(1)


4x2 — 2 (k + 1) x + (k + 4) = 0


d = b2 – 4ac


d = (–2 (k + 1)2 – 4 (4) (k + 4)


d = (– 2k – 2)2 – 16k – 64


d = 4k2 + 4 + 8k – 16k – 64


(∵ (a – b)2 = a2 + b2 – 2ab)


d = 4k2 – 8k – 60


From (1), d = 0


∴ Equation will be:


4k2 – 8k – 60 = 0


Dividing by 4


k2 – 2k – 15 = 0


4k2 – 5k + 3k – 15 = 0


k (k – 5) + 3(k – 5) = 0


(k – 5) (k + 3) = 0


K – 5 = 0 k + 3 = 0


K = 5 k = –3


More from this chapter

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6

Without finding the roots, comment upon the nature of roots of each of the following quadratic equations:

2x2— 6x + 3 = 0

 6

Without finding the roots, comment upon the nature of roots of each of the following quadratic equations:

2x2 — 5x — 3 = 0

 7

Find the value of k, so that the quadratic equation

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

 8

For what values of k, does the following quadratic equation has equal roots.

9x2 + 8kx + 16 = 0