GATE 2019 CS – Question 57
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2+6xY+3Y+6$ has only real roots is (rounded off to 1 decimal place) ________.
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Correct answer: 0.79 to 0.81
Explanation
The discriminant is $36Y^2-12(3Y+6)=36(Y^2-Y-2)=36(Y-2)(Y+1)\ge0$, which holds for $Y\ge2$ in $(1,6)$. The probability is $\frac{6-2}{5}=0.8$.