Question

What is a quadratic equation that has a root sum of 1 and product of -1?

Answer 1

`x^2-x-1=0`

Explanation:

Let
`x_1` and
`x_2` be the roots of the required quadratic equation.

Then the equation is formed using:

`x^2-(sum\:of\:roots)x+product\:of\:roots=0`

or

`x^2-(x_1+x_2)x+x_1*x_2=0`

From the given information, sum of the roots is:

`x_1+x_2=1` and the product is

`x_1x_2=-1`

Therefore the required equation is

`x^2-x-1=0`