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 of k is the number of dots on the upper face of the die. The probability that the equation will have real and 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 of k is the number of dots on the upper face of the die. The probability that the equation will have real and unequal roots is (A) (1/3) (B) (2/3) (C) (1/2) (D) (3/4)

Tardigrade Admin · Accepted Answer

D>0 ⇒ k2-4>0 k>2 ⇒ k= 3,4,5,6 P( text real unequal roots) =(4/6)=(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 of $k$ is the number of dots on the upper face of the die. The probability that the equation will have real and unequal roots is

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{3}{4}$

$D > 0 \Rightarrow k^{2} - 4 > 0$
$k > 2 \Rightarrow k = {3, 4, 5, 6}$
$P (real unequal roots) = \frac{4}{6} = \frac{2}{3}$

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 of k is the number of dots on the upper face of the die. The probability that the equation will have real and unequal roots is

31​

32​

21​

43​