Question

If x - 2 is a factor of x2 + ax + b and
a + b = 1, find the values of a and b.
​

Answer 1

p(x) = x² + ax + b.

Given that (x - 2) is a factor of p(x). So p(2) = 0.

$p(2) = (2)^2 + a(2) + b = 0 \\ \\ p(2) = 4 + 2 a + b = 0 \\ \\ \\ 4 + 2 a + b = 0 \\ \\ 2a + b = - 4 \\ \\ a + a + b = - 4 \\ \\ a + 1 = - 4 \ \ \ \ \ [\because \ a + b = 1] \\ \\ a = - 4 - 1 \\ \\ a = \bold{-5}$

Consider a + b = 1.

$a + b = 1 \\ \\ - 5 + b = 1 \\ \\ b = 1 + 5 \\ \\ b = \bold{6}$

Thus the values of a and b are -5 and 6 respectively.