The probability of choosing randomly a number c from the set 1,2,3, 9 such that the quadratic equation x^2+4 x+c=0 has real roots, is

Step-by-step solution

The quadratic equation x^2 + 4x + c = 0 has real roots if and only if its discriminant D 0 . The discriminant D is given by D = b^2 - 4ac . Here a = 1 , b = 4 , and c = c . Substituting the values, D = 4^2 - 4(1)(c) = 16 - 4c . For real roots, 16 - 4c 0 , which implies 4c 16 , or c 4 . The set of possible values for c is 1, 2, 3, 4, 5, 6, 7, 8, 9 , so the total number of outcomes is 9 . The values of c from the set that satisfy c 4 are 1, 2, 3, 4 . The number of favorable outcomes is 4 . The probability is Number o