Question

answed.............. .

Answer 1

In a quadratic equation, we know that:
If roots = α , β 
α + β = -b / a
α * β = c/a
But α = 5 * β
∴ α + β = -b/a
⇒ 5β + β = -6/5
⇒ 6β = -6/5
⇒β = -1/5

α * β = c/a
⇒ 5β * β = k/5
⇒ 5β² = k/5
⇒ 5 * ( -1/5 )² = k/5
⇒ 1/5 = k/5
⇒ k = 1

Answer 2

if one root is x then other will be 5x
so x+5x= -6/5

=>6x=-6/5

=>x=-1/5.....(i)

putting x=-1/5

in the polynomial we get

=>5×(-1/5)^2+6×-1/5+k=0

=>5/25+(-6/5)+k=0

=>1/5-6/5+k=0

=>k= 5/5

=>k=1

hope this helps you