Q.

If both the roots of the quadratic equation x2 -2kx + k2 +k -5 = 0are less than 5, then k lies in the interval

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away
An Intiative by Sri Chaitanya

a

-∞, 4

b

4, 5

c

5, 6

d

6, ∞

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

x2 - 2kx + k2 + k - 5 = 0  Roots are less than 5, D≥0 4 k2 - 4 (k2 + k - 5) ≥ 0       ..... (i) ⇒k≤5 ⇒f5 >0                     .....(ii) ⇒k ∈(-∞, 4) ∪ (5, ∞); -2k2 <5 ⇒k <5    ....(iii) form (i), (ii) and (iii), k ∈ (-∞, 4)
Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon
If both the roots of the quadratic equation x2 -2kx + k2 +k -5 = 0are less than 5, then k lies in the interval