Question

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if the equations x²+(k+1)x+k=0 and x²-(k+2)x+2k =0 have one root in common then values of k are:​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

2. , 1/2. Answer.

Step-by-step explanation:

let a. and 2a are the roots of x^2+(k+1).x+k=0.

a+2a=-(k+1)/1. or. a=-(k+1)/3……………….(1)

a×2a = k/1. or. 2a^2=k……………………………(2)

On putting a=-(k+1)/3. from eqn.(1)

2.{(k+1)^2}/9 =k

or. 2.(k+1)^2 = 9k

or. 2k^2+4k+2–9k=0

or. 2k^2–5k+2=0

or. 2k^2–4k-k+2=0

or. 2k(k-2)-1(k-2)=0

or. (k-2)(2k-1)=0

k= 2. , 1/2. Answer.