Question

Without finding discriminant show x^2+4 has no real roots

Answer 1

Hey there!

We are talking about roots, so x² + 4 = 0

=> x² + 4 = 0

=> x² = -4

=> x = √-4 = ±2i

We know that,

$\boxed{\boxed{Square \: root \: of \: a \: negative \: number \: is \: never \: real \: but \: a \: imaginary \: number.}}$

Hence, x² + 4 = 0 has no real roots , It has imaginary roots ( i. e, +2i , -2i )