Question

For what value of $c$ does the equation $\left(c-2\right)x^2+2\left(c-2\right)x+2=0$ posses no real roots?

Answer 1

$(C-2)x^2+2(C-2)x+2=0$

Should not have real roots

$\Rightarrow b^2<4ac$

$\Rightarrow \left[2\right(C-2){]}^2<4(C-2\left)\right(2)$

$\Rightarrow 4(C-2{)}^2<4(2\left)\right(C-2)$

$\Rightarrow (C-2{)}^2<2(C-2)$

$\Rightarrow (C-2)(C-2-2)<0$

$\Rightarrow (C-2)(C-4)<0$

$C$ should be between $2$ and $4$

$\Rightarrow C=3$

$\therefore$ if $C=3$

$(C-2)x^2+2(C-2)x+2=0$ will have no real roots.