1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider the equation x 2+ kx +1=0. A single fair die is rolled to determine the value of the middle coefficient, k. The value for k is the number of dots on the upper face of the die. The probability that the equation will have real, unequal roots, is

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Q. Consider the equation $x ^2+ kx +1=0$. A single fair die is rolled to determine the value of the middle coefficient, $k$. The value for $k$ is the number of dots on the upper face of the die. The probability that the equation will have real, unequal roots, is

Probability - Part 2

Solution:

The roots will be real and unequal when $b^2-4 a c>0$. For the equation above, we have $k ^2-4 \cdot 1 \cdot 1$, and so $k$ must be greater than 2 . The probability of this happening is $2 / 3$