Question

if (x-a) is a factor of
${x}^{3} - m {x}^{2 } - 2nax + n {a}^{2}$
prove that a= (m+n).


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Answer 1

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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.