how come. X square + 1 = 0 has no real roots

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By using the method of completing the square, show that the equation $2 x^{2} + x + 4 = 0$ has no real roots.

Q. By using the method of completing the square show that

{4 x}^{2} + 3 x + 5 = 0

has no real roots.

Question 11.
$(x^{2} + 1)^{2} - x^{2} = 0$ has:

(a) four real roots

(b) two real roots

(d) one real roots

x^{2} + 5 k x + 16 = 0

has no real roots, then :

Question 8
The quadratic equation $2 x^{2} - \sqrt{5} x + 1 = 0$ has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots

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