JEE Main 2013 Mathematics question on Complex Numbers and Quadratic Equations
If the equations x2+2x+3=0 and ax2+bx+c=0, a,b,c∈R have a common root, then a:b:c is
A.
1:2:3
B.
3:2:1
C.
1:3:2
D.
3:1:2
Show answer and solution
Correct option: A
Solution
The discriminant of x² + 2x + 3 = 0 is 4 - 12 = -8 < 0, so its roots are complex (non-real). Since a, b, c ∈ R, complex roots of the second equation must occur in conjugate pairs. Therefore both roots of x² + 2x + 3 = 0 are also roots of ax² + bx + c = 0, meaning the two equations have the same roots. This forces ax² + bx + c = k(x² + 2x + 3) for some real k, giving a : b : c = 1 : 2 : 3.
[JEE Main 2013]
Practise Complex Numbers and Quadratic Equations the way it is asked
A timed set of real JEE Main Complex Numbers and Quadratic Equations questions, graded as the exam grades. No sign-up.
