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If sin theta and cos theta are the roots...

If `sin theta and cos theta` are the roots of the equation `ax^2-bx+c=0`, then `a, b and c` satisfy the relation

A

`a^(2)+b^(2)+2ac=0`

B

`a^(2)-b^(2)+2ac=0`

C

`a^(2)+c^(2)+2ab=0`

D

`a^(2)-b^(2)-2ac=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that , `sinthetaandcostheta` are the roots of the equation `ax^(2)-bx+c=0`,
So `sintheta+costheta=(b)/(a)andsinthetacostheta=(c)/(a)`.
Using the indentity `(sintheta+costheta)^(2)=sin^(2)theta+cos^(2)theta+2sinthetacostheta`, we have
`(b^(2))/(a^(2))=1+(2c)/(a)rArra^(2)-b^(2)+2ac=0`
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