Quadratic Polynomial help plz (1 Viewer)

[physician]

k i've been trying to do this question but can't seem to find a solution..

i have the feeling there's an easy simple solution but i've allready used up like 4 pages of working out... and can't seem to find the answer... I'd aprecite any help

( Q ) If a and b ( alpha and beta) are the roots of x² + hx + k = 0, find the relationship between h and k if:

a (alpha) = 2b (beta)

I'll provide u with the answer for ur conveniance

k= (2/9) h²

any help would be greatly appreciated

 

[shafqat]

k i've been trying to do this question but can't seem to find a solution..

i have the feeling there's an easy simple solution but i've allready used up like 4 pages of working out... and can't seem to find the answer... I'd aprecite any help

( Q ) If a and b ( alpha and beta) are the roots of x² + hx + k = 0, find the relationship between h and k if:

a (alpha) = 2b (beta)

I'll provide u with the answer for ur conveniance

k= (2/9) h²

any help would be greatly appreciated

ab = k (products of roots)
a + b = -h (sum of roots)
k = 2b^2 (sub given into first eq)
-h = 3b (sub given into second)
h^2 = 9b^2
h^2(2/9) = b^2

so k= (2/9) h²

 

[physician]

ab = k (products of roots)
a + b = -h (sum of roots)
k = 2b^2 (sub given into first eq)
-h = 3b (sub given into second)
h^2 = 9b^2
h^2(2/9) = b^2

so k= (2/9) h²

i dont get how u went from: h^2 = 9b^2
to get: h^2(2/9) = b^2

were did 2/9 come from wouln't it be h²/9 ?

i understand the rest...

 

[physician]

oh wait... it's because k = 2b^2 right?

 

[physician]

thanks alot k3tan and shafqat

can't believe how easy it was.. thanks guys... "kicks himself in the head"