Find the Value of k in a Quadratic Equation so that One Root is Half the Other

[herodecesaire]

Great I love it as always. Well done !! I have learned new things. Thanks a lot.

[devondevon]

Answer k=9 and k=-9 as both will give a root of 3 and 6 or -3 and -6 in which one root is twice the other.
6:42 x^2-kx+18=0
(x-a) (x-2a) or ( x+a) (x+2 a) as both will give result with the constant being (positive) +18
using (-a)(-2a) =+18, then
2a^2= 18
a^2 = 9 (dividing both sides by 2)
a = 9^0.5
a = +3 and -3
Therefore 2a= 6 or -6 So:
(x-3)(x-6) and (x+3)(x+6)
using (x-3)(x-6) gives x^2-9x+18, so k=-9
AND using (x+3)(x+6) gives x^2+9x+18, so k=+9
Answer k= -9 or k=9
Note if you plugged -3 and -6 into (x-a)(x-2a) you get {x-(-3)}{x-(-6) or (x+3)(x+6)
And if you plugged +3 and +6 into it you get (x-3)(x-6)
And if you plugged -3 and -6 into (x+a)(x+2a) you get (x-3)(x-6)
And if you plugged +3 and +6 into it you get (x+3)(x+6)
So you are either going get (x+3)(x+6) or (x-3)(x-6) and k= 9 or +9

[devondevon]

Answer =15
(x-5)(x-10)
x^2-15x+50
k=15

[samarthh]

Answer for the question at end is if alpha is -3 then k -9 and if alpha is 3 then k is 9

[zaidzlni]

how if Find the k value in a Quadratic Equation so that One Root is negative the other