## Question

If m is a natural such that *m* ≤ 5, then the probability that the quadratic that the quadratic equation *x*^{2} + *mx* + has real roots is

### Solution

3/5

Discriminate *D* of the quadratic equation

Is given by

Now, *D* ≥ 0 ⇔ (*m* – 1)^{2} ≥ 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

#### SIMILAR QUESTIONS

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