Question

if alpha nd beta are zeroes of polynomial x²h3x+k such that alpha is equal to 2 beta fink k ​

Answer 1

alpha+ beta=-b/a

given that: alpha=2beta....(1)

so,

2beta+beta=-(-3)

3beta=3

beta=3/3

beta=1(use this value in eq1)

we get,

alpha=2

now,

alpha*beta=c/a

2*1=k

k=2 is the answer

Answer 2

Given alpha and beta are zeroes of polynomial f(x) = x^2-3x+k . We know ax^2+ bx+ c =0 .

Then alpha + beta= -b/a and alpha× beta= c/a . In this case

alpha+ beta= 3

3beta= 3. ( Given alpha= 2beta)

Beta=1 .

and Alpha× beta= c/a.

2beta×1 = k

k= 2 beta ( and since beta= 1 then alpha+ beta= 1 ,alhpa =2 ) we get k = 2.I hope my answer help you.