If x2 + 1 has no zeroes then ‘x’ is a A) Real numberB) Natural nu

1.	If x2 + 1 has no zeroes then ‘x’ is a A) Real numberB) Natural number C) Not Real D) Integer
Answer» Correct option is (C) Not Real \(\because\) \(x^2\geq0\) \(\Rightarrow\) \(x^2+1\geq1\) \(\Rightarrow\) \(x^2+1>0\) Hence, \(x^2+1\) never gives a zero for any real number, but if \(x^2+1\) has a zero then x never be a real number. Hence, if \(x^2+1\) has a zero then x is not a real number. Correct option is C) Not Real

If x2 + 1 has no zeroes then ‘x’ is a A) Real numberB) Natural number C) Not Real D) Integer

Answer»

Correct option is (C) Not Real

\(\because\) \(x^2\geq0\)

\(\Rightarrow\) \(x^2+1\geq1\)

\(\Rightarrow\) \(x^2+1>0\)

Hence, \(x^2+1\) never gives a zero for any real number, but if \(x^2+1\) has a zero then x never be a real number.

Hence, if \(x^2+1\) has a zero then x is not a real number.

Correct option is C) Not Real