Question

show that polynomial x^2-2x+5 has no real zeroes​

Answer 1

$x^2-2x+5\\a=1\\b=-2\\c=5\\D=b^2-4ac\\D=(-2)^2-4*1*5\\D=4-20\\D=-16$

We know that if Discriminant is smaller than zero then the quadratic equation have no real roots.