Question

If the equation 4y³ - 8a²yx² - 3ay²x + 8x³ = 0 represent three straight lines, two of them are perpendicular then sum of all possible values of a is

(A)  - 3/4

(B)  5

(C)  4/5

(D)  -3

Answer 1

Correct option  (A)  - 3/4

Explanation:

Let 4m³  - 3am² - 8a 2m + 8 = 0 has three roots m₁ , m₂ , m₃

⇒ m₁m₂m₃ =  - 2

Given m₁m₂ = - 1

⇒ m₃ = 2

⇒ 32 - 12a - 16a² + 8 = 0

⇒ 16a² + 12a - 24 = 0

Sum of values of a = - 12/16 = 3/4