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To find the answer, you need to equate the value of the polynomial at polynomial to 0 at p=k.

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the given polynomial is f(p) = p³ - k²p + p + 2

if k is a root of the polynomial,

then f(k) = 0

⇒ k³ - k²×k + k + 2 = 0

⇒ k³ - k³ + k + 2 = 0

⇒ k + 2 = 0

⇒

So the value of k is

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the given polynomial is f(p) = p³ - k²p + p + 2

if k is a root of the polynomial,

then f(k) = 0

⇒ k³ - k²×k + k + 2 = 0

⇒ k³ - k³ + k + 2 = 0

⇒ k + 2 = 0

⇒

**k = -2**

So the value of k is

And K is a root of this polynomial, p = k ⇒ p-k =0

⇒ p³-k²p+p+2 =0

⇒ p(p²-k²)+p+2 = 0

⇒ p(p-k)(p+k)+p+2 = 0

⇒ p.(0)(p+k)+p+2 = 0

⇒ p+2 = 0

⇒ p = -2

and p = k,

therefore K = -2