If a and bare non-zero roots of x²+a x+b=0 then the least value of x ²+a x + b is

Step-by-step solution

As given a and bare the roots of the equat x²+a x+b=0 sum of roots, a+b=-a b =-2 a and product of roots, a b=b array l a b-b=0 b(a-1)=0 array if b=0 then a=0 if b 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 2 )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