Question

If x + 1 is HCF of x² + ax + 5 and x³ + 9x + b, then the value of a + b = ?

Answer 1

(x + 1) is HCF of x² + ax + 5 and x³ + 9x + b

we know, HCF means highest common value of two or more factors.
hence, (x + 1) is highest common value of both x² + ax + 5 and x³ + 9x + b .

it means (x + 1) is a factors of x² + ax + 5 and x³ + 9x + b . so, x = -1 is the root of both expression.

now, put x = -1 in x² + ax + 5
(-1)² + a(-1) + 5 = 0
1 - a + 5 = 0
a = 6

again, put x = -1 in x³ + 9x + b
(-1)³ + 9(-1) + b = 0
-1 -9 + b = 0
-10 + b = 0
b = 10

hence, (a + b) = 6 + 10 = 16