If x + 2 is a factor of x² + ax + 2b and a + b = 4, find the values of a and b

Video Explanation

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Given

Polynomial: f(x) = x² + ax + 2b

x + 2 is a factor of f(x)

a + b = 4

To Find

The correct values of a and b.

Solution

Since x + 2 is a factor of the polynomial, by the Factor Theorem:

f(−2) = 0

Step 1: Substitute x = −2

f(−2) = (−2)² + a(−2) + 2b

= 4 − 2a + 2b

So,

4 − 2a + 2b = 0

Dividing by 2:

2 − a + b = 0

⇒ b = a − 2   …(1)

Step 2: Use the Given Condition a + b = 4

a + (a − 2) = 4

2a − 2 = 4

2a = 6

a = 3

Step 3: Find b

b = a − 2

b = 3 − 2 = 1

Final Answer

a = 3 and b = 1

Correct Option

(b) a = 3, b = 1

Conclusion

Hence, if x + 2 is a factor of x² + ax + 2b and a + b = 4, then a = 3 and b = 1.