$\text{ If }a\text{ and }b(\ne 0)\text{ are roots of the equation }{x}^2+ax+b=0,\text{ then the least value of }{x}^2+ax+b(x\in R)\text{ is }$

$\text{ Since }a\text{ and }b\text{ are the roots of the equation }{x}^2+ax+b=0$

$\text{ Therefore, }a+b=-a\text{ and }ab=b$

$\text{ Now, }ab=b\Rightarrow (a-1)b=0\Rightarrow a=1(\because b\ne 0)$

$\text{ Putting }a=1\text{ in }a+b=-a\text{ , we get }b=-2\text{ , }$

$\Rightarrow x^2+ax+b=x^2+x-2=(x+1/2{)}^2-1/4-2=(x+1/2{)}^2 -9/4$

$\text{which has minimum value }-9/4\text{ . }$