BITSAT 2015 Paper

As given a and b are the roots of the equation
x2 + ax + b = 0
⇒ sum of roots, a + b = – a
⇒ b = – 2a ...(1)
and product of roots, ab = b
⇒ ab – b = 0
⇒ b (a – 1) = 0
if b = 0 then a = 0
if b ¹ 0 then a = 1 and b = – 2
so, the expression will be,
f (x) = x2 + x – 2
= x2 + 2 .

1

2

x + (

1

2

)2−(

1

2

)2 - 2
⇒ f (x) = (x+

1

x

)2−

9

4

So, f (x) will be minimum, if (x+

1

2

)2 = 0
i.e. when x =

1

2

⇒ minimum value of function = -

9

4