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

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

F(p) = p³-k²p+p+2 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