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Let a,b and c be distinct non-negative n...

Let a,b and c be distinct non-negative numbers and the vectors `ahati+ahatj+chatk,hati+hatk,chati+chatj+bhatk` lie in a plane, then the quadratic equation `ax^(2)+2cx+b=0` has

A

real annd equal roots

B

real and unequal roots

C

unreal roots

D

both roots real and positive

Text Solution

Verified by Experts

The correct Answer is:
A
`ahati+ahatj+chatk,hati+hatk and chati+chatj+bhatk` are coplanar
`therefore|(a,a,c),(1,0,1),(c,c,b)|=0impliesc^(2)-ab=0`
For equation `ax^(2)+2cx+b=0`
`D=4c^(2)-4ab=0`
So, roots are real and equal.
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