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Let f(x)=x^2+b1x+c1 andg(x)=x^2+b2x+c2. ...

Let f`(x)=x^2+b_1x+c_1` and`g(x)=x^2+b_2x+c_2`. When f(x)=0 then the real roots of f(x) are `alpha,beta` and when g(x)=0 then the real roots of g(x) are `alpha+h,beta+h`. Minimum value of f(x) is `-1/4` and when x=`7/2` then value of g(x) will be minimum.
Minimum value of g(x) is-

A

`-1/4`

B

-1

C

`-1/3`

D

`-1/2`

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Knowledge Check

  • Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is 1/4 and when x= 7/2 then value of g(x) will be minimum. Value of b_2 is-

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    -5
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    9
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    -7

  • Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is -1/4 and when x= 7/2 then value of g(x) will be minimum. Roots of g(x)=0 are-

    A
    3,-4
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    `-3,4`
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    `-3,-4`

  • The minimum value of f(x)=2x^(2)+x-1 is-

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    `(9)/(4)`
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    `-(9)/(8)`

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