Question

if c,d are the rootsof (x-a) (x-b) -k=0,then the roots of (x-c) (x-d+k=0are A: b, c. B:a,b. C,:a, c. D:a,d​

Answer 1

Answer:

Since α,β and γ are the roots of the equation(x−a)(x−b)(x−c)−d=0.

So we have

α+β+γ=a+b+c ...(1)

αβ+βγ+γα=ab+bc+ca ...(2)

αβγ=abc+d ...(3)

Similarly, for the equation (x−α)(x−β)(x−γ)+d=0, we have

α+β+γ=a+b+c (from (1))

αβ+βγ+γα=ab+bc+ca (from (2))

And αβγ−d=abc (from (3))

Therefore clearly a,b and c will be the roots of the equation (x−α)(x−β)(x−γ)+d=0.