CAT 2003 Slot 1 — QA Question 5
Basics (Functions)Easy
The number of non-negative real roots of 2x – x – 1 = 0 equals
Answer & solution
Correct answer: 2
- A
0
- B
1
2
- D
3
Solution
2x − x − 1 = 0
∴ 2x = x + 1
This equation indicates the intersection of an exponential curve, lying in the I and II quadrants, and a straight line.
∴ It can have two intersection points at the most.
In this case, we can find two intersection points by trial and error as x = 0 and x = 1
∴ There cannot be any other point of intersection.
∴ The equation has 2 non-negative real roots.
Hence, option (c).