Question

find alpha such that x+alpha is a factor of p(x)=x4-alpha2x2+ 2x+alpha+3

Answer 1

Answer:

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Step-by-step explanation:

To Prove ⇒ α = m + n

Proof ⇒

Given condition ⇒

(x - α) is the factor of x³ - mx² - 2nαx + nx².

Using the Remainder Theorem, If (x - α) is the factor of the given polynomial, then the Remainder is equal to zero.

Now,

x - α = 0

x = α

Now,

f(α) = α³ - m(α)² -2nα² + n(α)²

0 = α³ - mα² - 2nα² + nα²

0 = α³ -mα² - nα²

α³ - α²(m + n) = 0

α³ = α²(m + n)

α = m + n

Hence Proved.

Hope it helps.

Answer 2

Step-by-step explanation:

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