Compare using the quadratic formula to find solutions to a quadratic equation having irrational roots to that of one that has rational roots.

For a general quadratic equation with rational coefficients

the two solutions are:

where D is the determinant.

Clearly, a solution will a rational number as long as is rational. However, it can be shown that a square root of an integer is only rational if its value is an integer. In other words, is rational if and only if the determinant is a perfect square, , otherwise the square root is irrational. Therefore the coefficients of quadratic equations that are to have rational solutions must satisfy the following condition:

use formula for the circle a=3.14

step-by-step explanation:

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a