Given equation, x2−4x−log10N=0 Roots of the equation will be real only, when the discriminant (D)≥0. For ax2+bx+c=0,D=b2−4ac For x2−4x−log10N=0 a=1,b=−4 and c=−log10N ∴b2−4ac≥0[∵ roots are real ( given )] ⇒(−4)2−4(1)(−log10N)≥0 ⇒16+4log10N≥0 ⇒4log10N≥−16 ⇒log10N≥−4 ⇒N≥(10)−4 [on taking ⇒ anti-logarithm] ⇒N≥
1
10000
⇒N≥0.0001 Hence, the minimum value of N is 0.0001.