Question

if x minus 2 is the factor of x square + a x + 2 b and a + b is equal to 4 then​

Answer 1

Step-by-step explanation:

Let p(x) =x^+ax+2b

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

Then by factor theorem

P(2)=0

=>2^+a(2)+2b=0

=>4+2a-2b=0

=>4+2(a-b)=0

=>2(a-b)=4

=>a-b=2.......(1)

Also given that a+b=4........(2)

Adding (1)&(2) we get.

a-b=2

a+b=4

2a =6

a=3

Putting the value of a in eqn (1)

a+b=2

3+b=2

b =2-3

b=-1