example 2 solve the equation a 2x 4 162 solution a text example solve x4 6x2 8x 24 0 example 3 solve an equation with imaginary solutions solve x 2 4x 5 text example find all zeros of f x x4 4x3 example 5c multiplying complex numbers solve for x find the values of x and y that make each equation true find the 4th root of the real number 81 14 solve example 5 solving using diffe methods solve 𝒙 𝟐 𝟖𝟏 𝟎 over the set of complex numbers factor x 4 6x 2 27 10 there 11 solve 2 log functions 5 the dimensions 10 x find the values of x and y that make each equation true ch 4 6 i can define and use imaginary and complex numbers and solve quadratic quadratic equations with complex solutions 5 simplify to simplify means to find x in the equation x 4 81 solution 3 square root of 81 9i square root of 20 2i 4 complex numbers 6 11 solve the equation using nth roots 2x 4 162 x 4 81 x 4 34 x 3 x 2 3 10 x 4 15 solving radical equations holt mcdougal algebra 1 8 9 the quadratic formula and the discriminant check it out 76 example 3c x4 1 80 x4 81 x 3 so the solution set is 3 3 find the number of solutions of each equation using the discdriminant solve for x write original equation x2 36 0 x2 36 x 6 or x 4 practice solving radical equations 7 you can also solve equations using imaginary numbers example 4 3x 2 48 0 example 5 x 2 81 example 6 3x 2 75 0 you can also solve equations using imaginary numbers quadratic equations with complex solutions notation note when an imaginary number an error occurred 2 5 6 quadratic equations and complex numbers 5 6 quadratic equations and complex numbers objectives classify and find all roots of a quadratic equation solution in this example the conjugate of the denominator is 1 2i multiply by 1 in the form 1 2i 1 2i to express this complex number elementary algebra v 1 0 elementary algebra v 1 0 neither of these equations had a variable with a coefficient of one in this case solving by substitution is not the best method substitute x 4 into the original equation to find the corresponding y value both of these values are restrictions of the original equation hence both are extraneous