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

Question

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 (A) 1 / 3 (B) 2 / 3 (C) 3 / 4 (D) 4 / 3

Tardigrade Admin · Accepted Answer

The roots will be real and unequal when b2-4 a c>0. For the equation above, we have k 2-4 ⋅ 1 ⋅ 1, and so k must be greater than 2 . The probability of this happening is 2 / 3

Q. Consider the equation $x^{2} + k x + 1 = 0$ . 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

$1/3$

$2/3$

$3/4$

$4/3$

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 $2/3$

Q. Consider the equation x2+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

1/3

2/3

3/4

4/3