Question

Find the values of ${}^{\prime }{k}^{\prime }$ for which $x^2-2x+k=0$ has real roots.

Answer 1

Given : The equation has real roots.

Discriminant $\Delta =b^2-4ac>0$ where $a=1,b=-2,c=k$

$\Rightarrow {(-2)}^2-4\times 1\times k>0$

$\Rightarrow 4-4k>0$

$\Rightarrow 4(1-k)>0$

$\Rightarrow k-1<0$

$\Rightarrow k<1$

$\therefore k\in (-\infty ,1)$