Let C and K be constants. If x² + Kx + 5 factors into (x + 1) (x + C), the value of K is -

Question: Let C and K be constants. If x² + Kx + 5 factors into (x + 1)(x + C), the value of K is -

Solution:
(x + 1)(x + C)
= x² + x + Cx + C
= x² + (1 + C)x + C.
Compare it with x² + Kx + 5
We find, C = 5 and K = C + 1
K = 1 + C
⇒ K = 1 + 5
∴ K = 6