1. Tardigrade
  2. Question
  3. Mathematics
  4. If a2+b2+c2+a b+b c+c a ≤ 0, where a, b, c ∈ R, then domain of the function f(x)=√ operatornamesgn(x) ⋅(a x2+b x+c) will be

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Q. If $a^2+b^2+c^2+a b+b c+c a \leq 0$, where $a, b, c \in R$, then domain of the function $f(x)=\sqrt{\operatorname{sgn}(x) \cdot\left(a x^2+b x+c\right)}$ will be

Relations and Functions - Part 2

Solution:

$ \Theta a^2+b^2+c^2+a b+b c+c a \leq 0 $
$\Rightarrow(a+b)^2+(b+c)^2+(c+a)^2 \leq 0$
$\Rightarrow a+b=b+c=c+a=0 \Rightarrow a=b=c=0 $
$\therefore D_f=R$