If `ax^(2)+bx+c=0` and `5x^(2)+6x+12=0` have a common root where a, b and c are sides of a triangle `ABC`, then (A) `Delta ABC` is obtuse angled (B) `Delta ABC` is acute angled (C) `Delta ABC` is right angled (D) no such triangle exists

Options

A. `Delta ABC` is obtuse angled
B. `Delta ABC` is acute angled
C. `Delta ABC` is right angled
D. no such triangle exists

Answer

D

Explanation

If `ax^(2)+bx+c=0` ………….
`5x^(2)+6x+12=0`
`D=36-4xx60= -240 lt 0`
`implies "roots of" 5x^(2)+6x+12=0` are imaginary
`:.` both the roots are common
`:. (a)/(5)=(b)/(6)=(c )/(12)=k`
`implies a = 5k, b = 6k, c = 12k`
since `a+blt c`
`:.` triangle is not formed