Question

If both the roots of the quadratic equation

x² –2kx + k² + k –5 = 0 are less than 5, then k lies in the interval

• A. (5, 6]
• B. (6, )
• C. (–, 4)
• D. [4, 5]

Answer 1

Answer: (C)

(–, 4)

Answer 2

(i) D ³ 0 ; (ii) F(5) > 0 ; (iii) – $\frac{b}{2a}$< 5

D ³ 0 Ž 4k² – 4(k² + k –5) ³ 0 – k + 5 ³ 0 k £ 5

f(5) = 25 –10 k + k² + k –5 = 0

k² –9k + 20 > 0

(k –4) (k –5) > 0

k Ī (, 4) Č (5, )

\ –$\frac{b}{2a}$< 5

k < 5 Ž (–, 5)

Hence k Ī (–, 4)