Question

It m is a natural such that m £ 5, then the probability that the quadratic equation x²+mx+ $\frac { 1 } { 2 }$ + $\frac { \mathrm { m } } { 2 }$ = 0 has real roots is-

• A. 1/5
• B. 2/3
• C. 3/5
• D. 1/5

Answer 1

Answer: (C)

3/5

Answer 2

Discriminant D of the quadratic equation

x² + mx + $\frac { 1 } { 2 }$ + = 0 is given by

D = m² – 4 $\left( \frac { 1 } { 2 } + \frac { m } { 2 } \right)$ = m² – 2m – 2 = (m – 1)² – 3

Now, D ³ 0 Ū (m – 1)² ³ 3

This is possible for m = 3, 4 and 5. Also, the total number of ways of choosing m is 5.

\ Probability of the required event = 3/5