Find the quadratic equation if roots are a/b,-b/a
Answers
Answer:
If α and β are the roots of the equation x2+8x−5=0, find the quadratic equation whose roots are αβ and βα.
My working out so far: I know that α+β=−8 and αβ=−5 (from the roots) and thenIi go on to work out that α=−8−β and β=−8−α, then I substitute into what the question asks me.
−8−β−8−α and −8−α−8−β however I do not know how to proceed further. I might be doing this completely wrong and my apologies for that.
Another solution came to me that if α and β are roots of the other unknown equation. I can somehow manipulate that to find the answer. But I don't think that will work. All help is appreciated thank you.
Answer:
abx²-(a²-b²)x-ab = 0
Step-by-step explanation:
α = a/b. β = -b/a
α+β = a/b-b/a = (a²-b²)/ab
αβ = (a/b)(-b/a) = -1
quadratic equ,
x²-(α+β)+αβ = 0
x²-[(a²-b²)/ab]x-1 = 0
abx²-(a²-b²)x-ab = 0