Complex Numbers And Quadratic Equations question 179
Question: If both the roots of the quadratic equation $ x^{2}-2kx+k^{2}+k-5=0 $ are less than 5, then $ k $ lies in the interval [AIEEE 2005]
Options:
A) $ (-\infty ,4) $
B) [4, 5]
C) (5, 6]
D) (6, $ \infty $ )
Show Answer
Answer:
Correct Answer: A
Solution:
$ x^{2}-2kx+k^{2}+k-5=0 $ Roots are less than 5, $ D\ge 0 $ $ 4k^{2}-4(k^{2}+k-5)\ge 0 $ ??(i)
Þ $ k\le 5 $
Þ $ f(5)>0 $ …..(ii)
Þ $ k\in (-\infty ,4)\cup (5,\infty ) $ ; $ -( \frac{2k}{2} )<5\Rightarrow k<5 $ …….(iii) form (i), (ii) and (iii), $ k\in (-\infty ,4) $
BETA
