Question

If `ax^2+bx+c=0 and cx^2 + bx+a=0(a,b,c in R)` have a common non-real roots, then which of the following is not true ?
A. `-2|a|lt |b| lt |a|`
B. `-2|c|lt b lt 2|c|`
C. `a=c`
D. None of these

Answer 1

Correct Answer - D
`(d)` `D_(1)=b^(2)-4ac lt 0`, `D_(2)=b^(2)-4ac lt 0`, as the root is non-real
`implies` Both roots will be common.
`implies (a)/(c )=(b)/(b)=(c )/(a)=1 implies a=c`
Now, `b^(2)-4ac lt 0impliesb^(2)-4a^(2)` ( or `4c^(2)`) ` lt 0`
`implies |b| lt 2 |a| ("or" 2|c |)`.