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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 2  - 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.

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