The number of integral values of k , for which one root of the equation 2 x 2 - 8 x + k = 0 lies in the interval 1 , 2 and its other root lies in the interval 2 , 3 , is :

Step-by-step solution

Let f ( x ) = 2 x 2 - 8 x + k = 0 f ( 1 ) > 0 f ( 2 ) < 0 f ( 3 ) > 0 Now, f ( 1 ) > 0 ⇒ 2 - 8 + k > 0 ⇒ k > 6   . . . . . . ( 1 ) f ( 2 ) < 0 ⇒ 8 - 16 + k < 0 ⇒ k < 8   . . . . . . ( 2 ) f ( 3 ) > 0 ⇒ 18 - 24 + k > 0 ⇒ k > 6   . . . . . . ( 3 ) From equations 1 ,   2   &   3 , k ∈ ( 6 , 8 ) ∴ Integral value of k = 7 Therefore number of integral value of k is one