Mathematics
If mx2 - nx + 8 has x - 2 as a factor, then :
2m - n = 4
2m + n = 4
2n + m = 4
n - 2m = 4
Factorisation
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Answer
By factor theorem,
If x - a is the factor of polynomial f(x), then remainder f(a) = 0.
Given,
x - 2 is a factor of mx2 - nx + 8.
Then substituting x = 2 in polynomial we get, remainder = 0 :
⇒ m(2)2 - 2n + 8 = 0
⇒ 4m - 2n + 8 = 0
⇒ 2(2m - n + 4) = 0
⇒ 2m - n + 4 = 0
⇒ n - 2m = 4.
Hence, Option 4 is the correct option.
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