Question

If (fx) = (x2 + 3x + a), g(x) = (x² + 5x + b), h(x) = (x2 + 4x + c) and LCM of [f(x), g(x), and h(c)] is (x + 1) (x + 2) (x + 3), then find (a - b + c).​

Answer 1

p(x)=x

2

−5x+a

q(x)=x

2

−3x+b

Given that HCF(p(x),q(x))=x−1, the other factors of p(x) and q(x) become (x−4) and (x−2) respectively.

∴p(x)=(x−1)(x−4)

q(x)=(x−1)(x−2)

⇒k(x)=LCM(p(x),q(x))=(x−1)(x−2)(x−4)

⇒(x−1)+k(x)=(x−1)+(x−1)(x−2)(x−4)

=(x−1)(x

2

−6x+8+1)

=(x−1)(x

2

−6x+9)

=x

3

−7x

2

+15x−9

So, by applying the relation between the coefficients and the roots , we get sum of roots=7.

Sum of roots is thus 7,

hope it helps you please mark me as brainliest