Question

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

Answer 1

Answer:

hi

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Step-by-step explanation:

Let p(x)=x

2

+ax+2b

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

Then by factor theorem

p(−2)=0

⇒(−2)

2

+a(−2)+2b=0

⇒4−2a+2b=0

⇒a−b=2 ---(i)

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