All Exams Test series for 1 year @ ₹349 only
Question

If the roots of the equation x 2 - 4x - log 10 N = 0 are real, then what is the minimum value of N ?

This question was previously asked in
CDS II 2021 General Knowledge Previous Year Paper (14-Nov-2021)
The correct answer is

0.0001

Given:

Roots of x 2 - 4x - log 10 N = 0 are real

Formula used:

Roots of quadratic equation ax 2+ bx + c = 0 are real 

if D ≥ 0  i.e b 2- 4ac ≥ 0 

And lf log aN = x

Then N = a x

Calculation:

We have the quadratic equation x 2 - 4x - log 10 N = 0

On comparing this equation with ax 2 + bx + c = 0, we get 

a = 1, b = -4 and c = - log 10 N

Now, According to the question 

D = b - 4ac  ≥ 0

⇒ (- 4) 2- 4 × 1 × (- log 10 N) ≥ 0

⇒ 16 + 4log 10 N ≥ 0

⇒ 4log 10 N ≥ -16

⇒ log 10 N ≥ - 4

⇒ N ≥ 10 -4

⇒ N ≥ 0.0001

∴ The minimum value of N is 0.0001.

Was this answer helpful?

Similar Questions

  1. If log 10 x+ log 10 x2 = 2 log 10 x + 1, then what is the value of x?

  2. If 5 x -1= (2.5) log 10 5, then what is the value of x ?

  3. If 6 3 - 4x 4 x + 5  = 8 (Given log 10 2 = 0.301 and log 10 3 = 0.477), then which one of the following is correct?

  4. If log x = 1.25 and y = x log x , then what is log y equal to?

  5. What is the value of log 10 (cos θ) + log 10 (sin θ) + log 10 (tan θ) + log 10 (cot θ) + log 10 (sec θ) + log 10 (cosesc θ)?

  6. If log 10 1995 = 3.3000, then what is the value of (0.001995) 1/8 ?

  7. Let XYZ be an equilateral triangle in which XY = 7 cm. If A denotes the area of the triangle, then what is the value of log 10 A4 ? (Given that log 10 1050 = 3.0212 and log 10 35 = 1.5441)

  8. What is the number of digits in 7 25 , 8 23 and 9 20 respectively? [Given log 10 2 = 0.301, log 10 3 = 0.477, log 10­­ 7 = 0.845]

  9. If log 10 2 = 0.3010 and log 10­ 3 = 0.4771, then the value of log 100 (0.72) is equal to

  10. There are n zeros appearing immediately after the decimal point in the value of (0.2) 25 . It is given that the value of log 10 2 = 0.30103. The value of n is


Important Questions from Special Functions

  1. The function $f(x) = [2x]$ where $[x]$ is the greatest integer function, is continuous at
  2. The number of real solutions of equation x 2 - 3 |x| + 2 = 0 is:

  3. If ϕ is the Euler’s Totient function, then ϕ(92) is:

  4. Consider the linear congruence 6 x ≡ 3 (mod 9). Then the incongruent solutions modulo 9 of this congruence are:

  5. If log10(x2 - 6x + 45) = 2, then the value of x are:

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
536 Tests 4 Tests Free
1647 Attempts
4.3(174)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App