#### Question

if x – 2 is a factor of x^{2} + ax + b and a + b = 1, find the values of a and b.

#### Solution

Let f(x) = x^{2} + ax + b

Since, (x – 2) is a factor of f(x).

∴ Remainder = f(2) = 0

(2)^{2} + a(2) + b = 0

4 + 2a + b = 0

2a + b = -4 …(i)

It is given that:

a + b = 1 …(ii)

Subtracting (ii) from (i), we get,

a = -5

Substituting the value of a in (ii), we get,

b = 1 – (-5) = 6

Is there an error in this question or solution?

Solution If X – 2 is a Factor of X2 + Ax + B and a + B = 1, Find the Values of a and B. Concept: Factor Theorem.