Find the zeroes of the given polynomial,p(x) = x4 – 16

1.	Find the zeroes of the given polynomial,p(x) = x4 – 16
Answer» Given p(x) = x⁴ – 16 is a biquadratic polynomial. It has almost two zeroes. Let p(x) = 0 ⇒ x⁴ – 16 = 0 ⇒ (x²)² – 4² = 0 ⇒ (x² – 4) (x² + 4) = 0 ⇒ (x + 2) (x – 2) (x² + 4) = 0 ⇒ (x + 2) = 0 or (x – 2) = 0 or (x² + 4) = 0 ⇒ x = -2 (or) x = 2 (or) x² = -4 Therefore the zeroes of the polynomial are 2, – 2, we do not consider √-4 since it is not real.

Answer»

Given p(x) = x⁴ – 16 is a biquadratic polynomial. It has almost two zeroes.

Let p(x) = 0

⇒ x⁴ – 16 = 0

⇒ (x²)² – 4² = 0

⇒ (x² – 4) (x² + 4) = 0

⇒ (x + 2) (x – 2) (x² + 4) = 0

⇒ (x + 2) = 0 or (x – 2) = 0 or (x² + 4) = 0

⇒ x = -2 (or) x = 2 (or) x² = -4

Therefore the zeroes of the polynomial are 2, – 2, we do not consider √-4 since it is not real.

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