Question

1, Ifx=1 andx=2 are solutions of equationsx + ax +bx+c=0
and a + b = 1, then find the value of b,​

Answer 1

Answer:

If x=1 and x=2 are roots of the polynomial P(x)= x3+ax2+bx+c , then P(x) can be factored as (x−1)(x−2)(x−α).

Multiplying, and equating to the coefficients of the powers of x in P(x) , we get

x3−x2(3+α)+x(2+3α)−2α=x3+ax2+bx+c

So, we get 3 equations:

−(3+α)=a

2+3α=b

−2α=c

Adding the first two, and using the given a+b=1 , we get α=1. So,

a=−4,b=5 and c=−2. P(x)=x3−4x2+5x−2