Question

Show that the polynomial x^2+2x+5 has ni real zeroes.​

Answer 1

Your Question:

Show that the polynomial x^2+2x+5 has no real zeroes.​

Your Answer:

The equation has no real zeroes when its Discriminant is less than zero

So if we are able to prove that the value of Discriminant is less than Zero than we can also prove that the polynomial has no real roots.

So, the formula of Discriminant is

$\tt D = b^2-4ac$

where D is discriminant

b is coefficient of x

a is coefficient of x^2

c is the constant

here

a = 1

b = 2

c = 5

So, finding discriminant now

$\tt D= b^2-4ac \\\\ \tt \Rightarrow D =(2)^2-4(1)(5) \\\\ \tt \Rightarrow D = 4 - 20 \\\\ \tt \Rightarrow D = -16$

So, here discriminant is less than zero. So no possible roots.