If the difference between the roots of the equation x^2+k x+1=0 is strictly less than 5 , where | k | 2 , then k can be any element of the interval

Step-by-step solution

Let the roots of the equation x ^2+ Kx +1=0 be , . Then, sum of roots, + =- K =+1 (Since, sum of roots of a x^2+b x+c=0 is -b a ; Product of roots is c a ) Given that, - 5 array ll & ( - )^2 5 & ( + )^2-4 5 & (-K)^2-4(1) 5 array array ll & K ^2-4-5 0 & ~K ^2-9 0 ~K ^2-3^2 0 ( ~K +3)( K -3) 0 & -3 K 3 & Also, it is given that | K | 2 & ~K -2 (i) & from K 2 (i), (ii), K (-3,-2] [2,3) array