Question 1172153
Find the quadratic equation in x with the given roots 1±3i√5 / 2 <- (it is a fraction). Show clear solution thanksss!
<pre>{{{(1 +- 3i*sqrt(5))/2}}} ====> {{{(- b +- sqrt(b^2 - 4ac))/(2a)}}}
As seen above, and based on the quadratic equation formula, 1 = - b___b = - 1
Also, as seen above, and based on the quadratic equation formula, {{{matrix(3,3, 2, "=", 2a, 2/2, "=", a, 1, "=", a)}}}
                                                                  {{{matrix(1,  5, 3i*sqrt(5), "=", sqrt(5 * - 9), "=", sqrt(- 45))}}}
Finally, as seen above, and based on the quadratic equation formula, the DISCRIMINANT, {{{matrix(1,3, b^2 - 4ac, "=", - 45)}}}
                                                                  {{{matrix (5,3, (- 1)^2 - 4(1)c, "=", - 45, 1 - 4c, "=", - 45, - 4c, "=", - 46,
c, "=", (- 46)/(- 4), c, "=", 23/2)}}}
                                                                  {{{matrix (1,3, ax^2 + bx + c, "=", 0)}}} <====== General form of a quadratic equation
                                                                  {{{matrix (1,3, x^2 - x + 23/2, "=", 0)}}} -------- Substituting 1 for a, - 1 for b, and {{{23/2}}} for c.
                                                                  {{{h ighlight_green(matrix(1,3, 2x^2 - 2x + 23, "=", 0))}}} ----- Multiplying the above by LCD, 2