Let `f(x)=x^2+b x+c ,w h e r eb ,c in Rdot` If `f(x)` is a factor of both `x^4+6x^2+25a n d3x^4+4x^4+28 x+5` , then the least value of `f(x)` is `2` b. `3` c. `5//2` d. `4`

Options

A. 2
B. 3
C. `5//2`
D. 4

Answer

4

Explanation

`f(x) = x^(2) + bx + c`
f(x) is factor of both `x^(4) + 6x^(2) + 25 and 3x^(4) + 4x^(2) + 28x + 5`
`therefore` f(x) will also be factor of
`3(x^(4) + 6x^(2) + 25) - (3x^(4) + 4x^(2) + 28x + 5) = 14(x^(2) - 2x + 5)`
`therefore x^(2) - 2x + 5` and f(x) have both roots common hence least value of
`f(x) = (x - 1)^(2) + 4 ge 4`