Question

α, β, γ are zeroes of cubic polynomial x3– 2x2 + qx – r.
         If α + β = 0 then show that 2q = r.​

Answer 1

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Answer 2

here your answer...

if you can see the sum of the roots is-b/a

that is a+b+c=-(-2)/1

and the sum of two roots is 0

so c=+2---------(1)

sum of product of two pair of consecutive roots = c/a

that is ab+bc+a=q/1

and abc=r that is -d/A

ab+c(a+b)=q

ab=q-----------(2)

abc=r====> q×c=r from eq.2

and from eq.1 we will get 2×q=r, hence proved .....