Question

The number of real solutions of the equation ${\left(\frac{5}{7}\right)}^2=-x^2+2x-3$ is equal to

• A. 2
• B. zero
• C. 1
• D. none of these

Answer 1

The correct option is B zero

${\left(\frac{5}{7}\right)}^2=-x^2+2x-3$
$\Rightarrow x^2-2x+3-\frac{25}{49}=0$
$\Rightarrow {49x}^2-98x+122=0$
Hence, $D={\left(98\right)}^2-4\left(122\right)\left(49\right)<0$
So, roots are imaginary.