The pair of straight lines represented by the equation (3 d x^2-5 x y+ (d^2-2 ) y^2=0 ). If the lines are perpendicular to each other, for how many values of (d ) this condition will be satisfied?

Step-by-step solution

Given, pair of straight lines is (3 d x^2-5 x y+ (d^2-2 ) y^2=0 ) Since, lines are perpendicular ( x^2 ) coefficient (+y^2 ) coefficient (=0 ) ( gathered 3 d+d^2-2=0 d^2+3 d-2=0 d= -3 9-4 (-2) 2 1 = -3 17 2 = -3+ 17 2 ( or )= -3- 17 2 gathered ) Number of possible value of (d ) are 2 Hence, option (b) is correct.