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Sneha sees a graph that never touches or crosses the $x$ -axis at any point.
Which of the following polynomials could it be?

Class 10Graphical Meaning of ZeroesAlgebra — Polynomials

A $p (x) = x^{2} + 1$
B $p (x) = x^{2} - 1$
C $p (x) = x - 1$
D $p (x) = x^{2} - 4$

Step-by-Step Solution

x^{2} + 1 = 0

gives

x^{2} = - 1

, which has no real solution, so its parabola never meets the

x

-axis. The others all have real zeroes.

Answer: A)

p (x) = x^{2} + 1

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