Correct option is (C) (x + 1)2 = 2(x – 3)
Standard form of quadratic equation is \(ax^2+bx+c=0,a\neq0.\)
(A) \((x-2)\,(x+1)=(x-1)\,(x+3)\)
\(\Rightarrow x^2-2x+x-2=x^2-x+3x-3\)
\(\Rightarrow x^2-x-2=x^2+2x-3\)
\(\Rightarrow 2x-3+x+2=0\)
\(\Rightarrow3x-1=0\) which is a linear equation.
(B) \(x^4-1=0\) which is a quartic equation.
(C) \((x+1)^2=2(x-3)\)
\(\Rightarrow x^2+2x+1=2x-6\)
\(\Rightarrow x^2+2x+1-2x+6=0\)
\(\Rightarrow x^2+7=0\) which is a quadratic equation.
(D) \(x^2+3x+1=(x-2)^2\)
\(\Rightarrow x^2+3x+1=x^2-4x+4\)
\(\Rightarrow7x-3=0\) which is a linear equation.
