Question

Find all values of $m$ for which the quadratic equation $x^2+2-2m=0$ have no real solutions

• A. $m<\frac{-1}{2}$
• B. $m<\frac{1}{2}$
• C. $m<\frac{-1}{4}$
• D. None of these

Answer 1

Answer: (A)

$m<\frac{-1}{2}$

Given,

$x^2+2-2m=0$

condition for quadratic equation to have no real solution:

$b^2-4ac<0$

$2^2-4\left(1\right)(-2m)<0$

$4+8m<0$

$8m<-4$

$m<-\frac{4}{8}$

$\therefore m<-\frac{1}{2}$