Question

find a and b if a+b=4 and x-2 is a factor of polynomial x2+ax+2b​

Answer 1

Step-by-step explanation:

let p (×) = x² + ax + 2b

if x + 2 is a factor of p (x)

then by factor Theroem

p ( - 2 ) = 0

( - 2 )² + a ( - 2 ) + 2b = 0

4 - 2a + 2b = 0

a - b = 2 ---- ( ii )

also given that a + b = 4 ---- ( ii )

Adiing (i) and (ii) we get

2a = 6

a = 3

putting a = 3 in (i) we get

a - b = 2

3 - b = 2

b = 1

therefore we get a = 3 and b = 1

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