Question

If 0 $<$ c $<$ b $<$a and the roots α,β of the equation are imaginary then

• A. (|α|+|β |)/2 =|α||β |
• B. |α|+|β |>2
• C. |α|+|β |<2
• D. None of these

Answer 1

The correct option is B

|α|+|β |>2

Since α=$\frac{-b+i\sqrt{4ac–b^2}}{2c}$ and β = $\frac{-b+i\sqrt{4ac–b^2}}{2c}$ $<$0

|α|=|β |=$\sqrt{\frac{b^2+4ac-b^2}{4c^2}}$= $\sqrt{\frac{a}{c}}$$<$1