Question

If a > b > c and the system of equation $ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0$ has a non trivial solution then both the roots of the quadratic equation $a{t}^2+bc+c$ are

• A. real
• B. of opposite sign
• C. positive
• D. complex

Answer 1

Answer: (A), (D)

The correct options are
A real
D complex

Given $a>b>c$

and the system of equation $ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0$ has a non trivial solution

then both the roots of the quadratic equation $a{t}^2+bc+c$ are have at least one positive root

$\therefore$ it will be both real and complex.