Question

Match each quadratic equation with its roots.

x^2+58=4 x^2+47=3 2x^2+50=4 2x^2+85=7


x=±2i√11


x=±i√39


x=±3i√6


x=±i√23

Answer 1

We are given the 4 quadratic equations and 4 solutions. We have to match each equation with its correct solution. The step by step solution of each equation is listed below with its correct answer at the end of the solution. First we have to isolate variable(x²) on one side of the equation and then we have to take square root of both sides to get the answer.

Equation 1:

`x^(2) +58=4\\\\x^(2) = 4 -58\\\\ x^(2) = -54\\\\ x = \pm √(-54)\\\\ x= \pm i √(54)\\\\ x=\pm i √(9 * 6)\\\\ x = \pm i \sqrt{3^(2) * 6}\\\\ x= \pm 3i√(6)`

Equation 2:

`x^(2)+47=3\\\\ x^(2)= 3 - 47\\\\ x^(2) =-44\\\\ x=\pm √(-44)\\\\ x=\pm i√(44)\\\\ x=\pm i√(4 * 11)\\\\ x=\pm 2i√(11)`

Equation 3:

`2x^(2) +50=4\\\\ 2x^(2) =-46\\\\x^(2) =-23\\\\ x=\pm √(-23)\\\\ x=\pm i√(23)`

Equation 4:

`2x^(2) +85=7\\\\ 2x^(2) =7-85\\\\ 2x^(2) =-78\\\\ x^(2) =-39\\\\ x=\pm √(-39) \\\\ x=\pm i√(39)`