SOLUTION: Find a quadratic equation whose roots differ by 1 and are reciprocals of each other. Find the roots of the equation. (Two answers.)
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-> SOLUTION: Find a quadratic equation whose roots differ by 1 and are reciprocals of each other. Find the roots of the equation. (Two answers.)
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You can put this solution on YOUR website! ind a quadratic equation whose roots differ by 1
a, b
a = b + 1
and are reciprocals of each other.
a =
then
b + 1 = 1/b
mult by b
b^2 + b = 1
b^2 + b - 1 = 0
Using the quadratic formula:
b = -1.618
b = +.618
Using the positive solution: a = 1.618
FOIL
(x+.618)(x+1.618) = x^2 + 2.236x + 1
Two roots using the quadratic formula:
x = -1.618
x = -.618
:
Check on calc 1/1.618 = .618, and 1/.618 = 1.618
