Question

Find a quadratic equation equation whose roots differ by 1 and are reciprocals of each other. Find the roots of the equation.

Answer 1

So you're solving the system
a-b=1
ab=1
?

Answer 2

yep

Answer 3

What do you have so far? That system yields a quadratic itself.

Answer 4

If a-b=1, then a=b+1 [a is larger root, b is smaller root)
-> ab=1=(b+1)b
-> b^2+b-1=0.

Can use quadratic formula to solve for b, then add 1 to that to get a.
With the two roots known, you can find a polynomial.