If x-a is a factor of (2x×x-mx+na),then prove that a=m-n÷2
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If (x-a) is a factor of 2x²-mx +na
Then equation the divisor to zero
i.e.
x-a = 0
⇒x=a
so, putting x= a will make the entire expression 2x²-mx +na to zero
∴2(a)² -ma +na =0
⇒a(2a -m+n) =0
as a ≠0
so, 2a - m+n =0
⇒a = (m-n)/2 (proved)
Then equation the divisor to zero
i.e.
x-a = 0
⇒x=a
so, putting x= a will make the entire expression 2x²-mx +na to zero
∴2(a)² -ma +na =0
⇒a(2a -m+n) =0
as a ≠0
so, 2a - m+n =0
⇒a = (m-n)/2 (proved)
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