Question

Suppose a, b, c, el such that greatest common divisor of x2 + ax +b and
x2 + bx+cis (x + 1) and the least common multiple of x2 + ax +b and x +bx+c
is (x - 4x2 + x + 6) Find the value of|a + b + c|​

Answer 1

Answer:

(6) x 2 +ax+b≡(x+1)(x+b)⇒b+1=a

also x

2 +bx+c=(x+1)(x+c)⇒c+1=b

or b+1=c+2

hence b+1=a=c+2

also (x+1)(x+b)(x+c)≡x

3 −4x 2 +x+6

⇒x 3 +(1+b+c)x 2 +(b+bc+c)x+bc≡x 3 −4x 2 +x+6

⇒1+b+c=−4

⇒2c+2=−4⇒c=−3;b=−2 and a=−1

⇒a+b+c=−6

Step-by-step explanation:

hope it helps