Question

. Determine the number of zeros of the polynomial x^4-1.​

Answer 1

Answer:

p(x) = x^4-1

x^4-1 =0

x^4= 1

x =1

Answer 2

The number of zeros of the given polynomial is 2.

Step-by-step explanation:

The given polynomial:

$x^{4}-1$

To find, the number of zeros of the given polynomial = ?

∴ $x^{4}-1$

$=(x^{2})^2-(1^{2})^2$

Using the algebraic identity,

$a^{2}-b^{2}=(a+b)(a-b)$

$=({x^{2}+1^{2})(x^{2}-1^{2})$

$=(x^{2}+1)(x+1)(x-1)$

x = 1 and - 1

$x^2+1$ is no real roots.

∴ The number of zeros of the given polynomial = 2

Hence, the number of zeros of the given polynomial is 2.