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Quadratic Polynomial help plz (1 Viewer)

physician

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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

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physician said:
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

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shafqat said:
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

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thanks alot k3tan and shafqat

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

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