Write a quadratic equation whose roots are the reciprocal of the roots of the equation x2 – 20x + 96 = 0.

x ^ 2 – 20x + 96 = 0.

In this quadratic equation for the roots of the equation x1 and x2, we write the following equalities:

x1 + x2 = – p = 20,

x1 * x2 = q = 96.

Having solved the quadratic equation using the discriminant, we get:

x1 = 8, x2 = 12.

For the new quadratic equation, the inverse roots of the obtained roots: x11 = 1 / x1 = 1/8, x22 = 1 / x2 = 1/12.

For the new equation, p = – (1/8 + 1/12) = – 5/24, q = (1/8 * 1/12) = 1/96.

Then the new quadratic equation with inverse roots to the given one has the form:

x ^ 2 – 5/24 + 1/96 = 0.