Question

if x-a is a factor of x³-mx²-2nax+na² then prove that a=m+n​

Answer 1

Answer:

If x3 + mx2 + nx + 6 has x - 2 as a factor and leaves a remainder 3, when divided by x - 3, find the values of m and n.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

Let p(x) = x³ - mx² - 2nax + na².

If (x - a) is a factor of p(x), then p(a) = 0

Now, p(a) = a³ - m(a)² - 2na(a) + na² = 0

⇒a³ - a²m - 2a²n + na² = 0

⇒. a³ - a²m - a²n = 0

⇒ a²(a - m - n) = 0

Since, a ≠ 0

∴ a - m - n = 0

⇒. a = m + n

Hence, proved.