If `ax^(2)+bx+4` attains its minimum value -1 at x = 1, then the values of a and b are respectively

Options

A. 5, -10
B. 5, -5
C. 5, 5
D. 10, -5

Answer

A

Explanation

Let `f(x)=ax^(2)+bx+4`
On differentiating w.r.t. x, we get
`f'(x)=2ax+b`
For minimum, put f'(x) = 0
`implies" "x=-(b)/(2a)`
Since, it is given that at x = 1 minimum value is -1.
`:." "1=-(b)/(2a)`
`implies" "2a+b=0" "...(i)`
and `f(1)=a+b+4=-1`
`implies" "a+b+5=0" "...(ii)`
On solving Eqs. (i) and (ii), we get a = 5, b = -10.