quadratic equation

Question

let x1>x2>x3>x4>x5>x6>0, and

A= x1+x2+.......+x6

B= x1x3+x3x5+x1x5+x2x4+x2x6+x4x6

C= x1x3x5+x2x4x6,

then the equation 2x^3 - Ax^2 + Bx - C = 0 has

1. exactly one real root

2. three positive roots

3. three negative roots

4. none of these

AYUSH SHARMA · Accepted Answer

THE CORRECT OPTION IS THREE REAL ROOTS.

let x1>x2>x3>x4>x5>x6>0, and

A= x1+x2+.......+x6

B= x1x3+x3x5+x1x5+x2x4+x2x6+x4x6

C= x1x3x5+x2x4x6,

then the equation 2x^3 - Ax^2 + Bx - C = 0 has

1. exactly one real root

2. three positive roots

3. three negative roots

4. none of these