Question

Check whether -2 and 2 are the zeroes of the polynomial x⁴- 16
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Answer 1

$\bigstar$ Question:

• Check whether (-2) and 2 are the zeroes of the polynomial x⁴ - 16.

$\bigstar$Given:

• The polynomial is x⁴ - 16 and we have to check whether 2 and (-2) are factors or not.

$\bigstar$To check:

• Whether (-2) and 2 are zeroes or not.

$\bigstar$ Solution:

Here, we will use remainder theorem.

p(x) = x⁴ - 16

Now, p(2) = (2)⁴ - 16

$\implies$ p(2) = 16 - 16

$\implies$ p(2) = 0

$\therefore$ 2 is a zero of the polynomial.

Now, p(-2) = (-2)⁴ - 16

$\implies$ p(-2) = 16 - 16

$\implies$ p(-2) = 0

$\therefore$ (-2) is also a zero of the polynomial.

Hence proved.

Answer 2

Answer:

Here, we will use remainder theorem.

p(x) = x⁴ - 16

Now, p(2) = (2)⁴ - 16

\implies⟹ p(2) = 16 - 16

\implies⟹ p(2) = 0

\therefore∴ 2 is a zero of the polynomial.

Now, p(-2) = (-2)⁴ - 16

\implies⟹ p(-2) = 16 - 16

\implies⟹ p(-2) = 0

\therefore∴ (-2) is also a zero of the polynomial.

Hence proved.