Question

if (x +2) is a factor of x^2 + ax +2b and a+b =4 ,then the values of 'a' is?

Answer 1

Answer:

a = 3

Step-by-step explanation:

Given :

• p(x) = x^2 + ax +2b. ..................(a)

• (x + 2) is a factor of p(x)

• a + b = 4. ..............(b)

To find: 'a'

• b = 4-a .................[by re-grouping (b)]

• substituting the value of 'b' in (a)

p(x) = x^2 + ax +2( 4-a)

= x^2 + ax + 8 - 2a. ................(c)

x= -2

(since 'x+2' is the factor, we can get the value of 'x'as -2)

• substituting it in (c)

(-2)^2 + (-2a) + 8 - 2a = 0

[by substituting the value of 'x' the answer will become zero- as it is said that 'x+2' is a factor of p(x)]

4 - 2a +8 - 2a = 0

12 - 4a = 0

12= 4a

a = 12/4

= 3

I hope this is helpfulI