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If ax^2+bx+c=0 and cx^2 + bx+a=0(a,b,c i...

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

Text Solution

Verified by Experts

The correct Answer is:
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 |)`.
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