Question

For what value of m, the roots of the equation $x^2-x+m=0$ are non real?

• A. $(\frac{1}{4},\infty )$
• B. $(-\infty ,\frac{1}{4})$
• C. $(-\frac{1}{4},\frac{1}{4})$
• D. None of these

Answer 1

The correct option is A $(\frac{1}{4},\infty )$

$x^2-x+m=0$ where $a=1,b=-1,c=m$

$D=b^2-4ac$

$=1-4m$

$D<0$ for not real:

$1-4m<0$

$4m>1$

$m>\frac{1}{4}=(\frac{1}{4},\infty )$