Question

If both (x + 2) and (2x + 1) are factors of ax^2 + 2x +b, then the value of a - b is
a. -1
b. 2
c. 1 d. 0​

Answer 1

Answer:

d.0

Step-by-step explanation:

(x+2) (2x+1)

x=-2 , x=-1/2

put the value in p(x)

4a+b=4....(1)

a+4b=4...(2)

(1)and(2) we get

a=4/5 and b=4/5

(a-b)=4/5-4/5=0

Answer 2

Answer:

$(d) \: 0$

Step-by-step explanation:

If (x+2) and (2x+1) are factors of ax² + 2x + b

Then,

x = - 2 or -1/2

Putting the value of x on ax² + 2x + b = 0

a(-2)² + 2×-2 + b = 0

4a - 4 + b = 0

4a + b = 4

And

a(-1/2)² + 2×-1/2 + b = 0

a/4 - 1 + b = 0

a/4 + b = 1

a + 4b = 4

Now,

4a + b = 4 } × 1

a + 4b = 4 } × 4

4a + b = 4

4a + 16b = 16

(-)....(-)....(-)

------------------------

- 15b = - 12

b = 4/5

Putting the value of b on a + 4b = 4

a + 4×4/5 = 4

a + 16/5 = 4

a = 4 - 16/5

a = 20 - 16 / 5

a = 4/5

Then the value of a - b =

4/5 - 4/5

0