Question

If the quadratic equations 3x² + ax + 1 = 0 and 2x² + bx + 1 = 0 have a common root then the value of 5ab − 2a² − 3b², where a, b ∈ R, is equal to 

(A)  0 

(B)  1 

(C)  −1 

(D)  None of these

Answer 1

Correct option (B) 1

3x² + ax + 1 = 0, 2x² + bx + 1 = 0 have a common root. Subtracting these equations, we get

x² + (a − b)x = 0

⇒ x = 0, x = (b − a)

Clearly the common root is (b − a), So

3(b − a) 2 + a(b − a) + 1 = 0

⇒ 3b² + 3a² − 6ab + ab − a² + 1 = 0

⇒ 5ab − 2a² − 3b² = 1