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Factorisation of Quadratic Polynomials - Factor Theorem

The polynomia...

Question

The polynomial equations $P_{1}$ (x) = $x^{3} + x^{2} + x + 1$ and $P_{2}$ (x) = $x^{2} + 1$ have how many zeroes in common?

A

1

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B

2

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C

3

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D

0

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Solution

The correct option is D
0

$P_{1}$ (x) can be factorized as $(x + 1) (x^{2} + 1)$ . So, There are two factors of $P_{1}$ (x) but $P_{2}$ (x) has no factors and hence it has no zeroes. So, there are no zeroes in common for $P_{1}$ (x) and $P_{2}$ (x).

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