Question

If x + 2 s a factor of x^2 +ax+ 2b and a + b = 4 then

1 point​

Answer 1

Full Question :–

If x + 2 is a factor of x² + ax + 2b and a + b = 4 then what is the value of a and b ?

Given :–

• Factor of x² + ax + 2b is x + 2.
• a + b = 4

To Find :–

• Value of a and b.

Solution :–

Let,

• p(x) = x² + ax + 2b ––––– (1)

So, x + 2 is factor of p(x)

⟹ x + 2 = 0

⟹ x = –2

Now, put the value of x in (1),

⟹ p(–2) = 0

⟹ (–2)² + a(–2) + 2b = 0

Now, open the bracket.

⟹ 4 – 2a + 2b = 0

⟹ –2a + 2b = –4

⟹ –2a + 2b = –4

⟹ –2(a – b) = –4

⟹ a – b = $\dfrac{\cancel{-4}}{\cancel{-2}}$

⟹ a – b = 2 ––––– (2)

Given that,

• a + b = 4 ––––– (3)

Adding both the equation (2) and (3), we get

⟹ (a $\cancel{-b}$ ) + (a $\cancel{+ b}$ ) = 2 + 4

⟹ a + a = 6

⟹ 2a = 6

⟹ a = $\dfrac{6}{2}$

⟹ a = 3

Now, put the value of a in equation (2), we get

⟹ a – b = 2

⟹ 3 – b = 2

⟹ 3 – 2 = b

⟹ 1 = b

Hence,

The value of a = 3 and b = 1.