If the numbers appeared on the two throws of a fair six faced die are α and β, then the probability that x²+α x+β>0, for all x R, is : [25-Jul-2022-Shift-1]

Correct Answer is : 1736\;17/363617

Correct Answer is : 1736\;17/363617

Test Index

Probability Part 2

Section: Mathematics

Question : 72 of 100

Marks: +1, -0

\alpha

\beta

x^{2}+\alpha x+\beta>0

x \in R

Solution: 👈: Video Solution

For

x^{2}+\alpha x+\beta>0 \forall x \in R

to hold, we should have

\alpha^{2}-4 \beta< 0

\alpha=1, \beta

can be

1,2,3,4,5

, 6 i.e., 6 choices

\alpha=2, \beta

can be

2,3,4,5,6

i.e., 5 choices

\alpha=3, \beta

can be

3,4,5,6

i.e., 4 choices

\alpha=4, \beta

can be 5 or 6 i.e., 2 choices

\alpha=6

, No possible value for

\beta

i.e., 0 choices

Hence total favourable outcomes

=6+5+4+2+0+0

=17

Total possible choices for

\alpha

and

\beta=6 \times 6=36

Required probability

=\;\frac{17}{36}

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