Question

If x - 2 is a factor for $x^2+ax+b$ and a + b = 1, find the values of a and b.

Answer 1

Let f(x) = $x^2+ax+b$
Since, (x – 2) is a factor of f(x).
Remainder = f(2) = 0
${\left(2\right)}^2$ + 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