Mathematics - Quadratic Equation Question with Solution | TestHub

$|x-a|=(x-1{)}^2$ Iff $a=x\pm (x-1{)}^2$ No of solutions $=$ no of intersection its between $y=a;f(x)=x^2-x+1$ and $g(x)=-x^2+3x-1$. clearly the graphs of $f(x),g(x)$ are tangents to each other at $A(1,1)$. The line $y=a$ intersects the two graphs at three points Iff it passes through one of the three pts $\mathrm{A},\mathrm{B},\mathrm{C}$. Here $B=\left(\frac{1}{2},\frac{3}{4}\right)$ vertex of f and $C=\left(\frac{3}{2},\frac{5}{4}\right)$ vertex of ' g ' i.e if $a\in \left\{\frac{3}{4},\frac{5}{4},1\right\}$