Question

If a and b are the non-zero distinct roots of $x^2+ax+b=0$, then the least value of $x^2+ax+b$ is

• A.
• B.
• C. -
• D. 1

Answer 1

The correct option is C -

Solution : a and b are root of $x^2+ax+b=0$
Sum of root :$a+b=-a,2a+b=0$
Product of root : $ab=b,b(a-1)=0$
$\{\begin{array}{cc}a=1& \\ b=-2& b\ne 0\end{array}$
Minimum value of $x^2+ax+b$ at $x=\frac{-a}{2}=\frac{-1}{2}$
$\equiv \frac{1}{4}+(-\frac{1}{2})-2=\frac{-9}{4}$