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Answer:
x^2+(x/4)-1
Step-by-step explanation:
(x-a)(x-b)=0
a and b are the roots
a+b=1/4
ab=-1 => a=-1/b
b-1/b = 1/4
b^2-1=b/4
b^2-b/4-1=0
b = (1/4+- sqrt(65/16))/2
plugging this into a results in
a = (1-sqrt(65))/8, b = (1+sqrt(65))/8
a = (1+sqrt(65))/8, b = (1-sqrt(65))/8
and then if you plug those into (x-a)(x-b)
you get
x^2+x*(1+sqrt(65)/8)+x*(1-sqrt(65))/8-(1+sqrt(65))/8*(1-sqrt(65))/8
which becomes
x^2+x/4-1
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