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If quadratic equation f(x)=x^(2)+ax+1=0 ...

If quadratic equation `f(x)=x^(2)+ax+1=0` has two positive distinct roots then

A

`f(1)gt0`

B

`f^(')(1)lt0`

C

`f(0)-f^(')(0)=2`

D

`f^(')(0)lt-2`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Let the roots be `alpha&beta`
`becausealphabeta=1impliesbeta=(1)/(alpha)`
sum of the roots `=alpha+(1)/(alpha)=-a`
`implies-age2impliesle-2`
`f(1)=2+a,f(0)=1`
`f^(')(x)=2x+a`
`f^(')(x)=ale-2,f^(')(1)=2+ale0`
`f(0)-f^(')(0)=1-age3`
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