Question

If (x – 1) (x + 2) is the H.C.F. of the polynomials
f(x) = (x2 – 5x + 4) (x2 + ax + b)
and g(x) = (x2 – 3 – 6) (x2 + 3x + b),​

Answer 1

Answer:

Answer:

Thus a=3 and b=4

Step-by-step explanation:

(x + 4)(x-2)(x + 1) is the HCF of the polynomials

f(x) = (x² + 2x-8)(x² + 4x + a) and

f(x)=(x+4)(x-2)(x² + 4x + a)

g(x) = (x2 - x-2)(x2 + 3x - b),

g(x) =(x-2)(x+1)(x2 + 3x - b)

common factor here in F(x) and g(x) is (x-2)

But HCF is  (x + 4)(x-2)(x + 1)

Thus f(x)  and g(x) have (x + 4)(x-2)(x + 1) as common factors

x-2 is already coomon in f and g

and  f(x) has already (x+4)

so x² + 4x + a has a factor   x+1

or x=-1

putting x=-1

(1)²+4*-1+a=0

1-4+a=0, a=3

similarly in g(x)

x2 + 3x - b has x+4 as a factor

so x=-4

puutingx=-4 we get

(-4)²+3*-4-b=0

16-12-b=0

4-b=0

b=4

Thus a=3 and b=4