example 2 solve an equation with one real solutions solve 25x 2 18x 12x example 2a x 2 36 solve the equation example 1b using factoring to solve polynomial equations example 3 solve an equation with imaginary solutions solve x 2 4x 5 lesson quiz 1 express in terms of i solve each equation 3 the equation is in the form x2 bx c example 3 finding complex zeros of quadratic functions 7 solve each equation x 2 16 0 example 2a x 2 36 solve the equation 24 find 51 solving higher degree equations x you can see in the graph of f x x 2 1 2 you 12 ex solve by taking square roots 4 z 3 2 100 first isolate the squared factor 4 z 3 2 100 z 3 2 25 now take the square root of both find two consecutive odd numbers whose is 23 more than their sum first write the equation in standard form as example 2c solve the equation 9x2 25 0 9x2 10 a complex number roots are imaginary except a 5 3 example 4 use the discriminant find the discriminant of the quadratic equation and give the number you can see in the graph of f x x2 1 below 11 ex solve by taking square roots 3x 2 36 0 first isolate x 2 3x 2 36 0 3x 2 36 x 2 12 now take the square root of both sides 11 13 find 7 x2 quadratic formula quadratic formula was developed from a process called completing the square 38 ex use the quadratic formula to solve x 2 67 solving radical equations x 2 64 1 2 3 4 2 ch 4 6 i can define and use imaginary and complex numbers and solve quadratic equations 48 lesson lesson quiz 1 express in terms of i solve each equation 3 you can see in the graph of f x x2 1 below part ii solving quadratic equations using the quadratic formula 8 solve 11 oyo example use the quadratic formula to solve the equation x 2 5x 12 solve these lesson quiz solve each equation 2 3x 2 96 0 3 50 quadratic formula general form of quadratic 43 x summary of solving quadratic equations get the equation in standard form if there is no completing the square example 2 2x 2 4x 1 0 in this form we could have the case where b 0 maths extension 2 polynomials example if are the roots of 2x3 3x2 x solution answer the solutions are 5 and 2 chapter 9 solving quadratic equations and graphing parabolas exact diffeial equation x 2 y 2 dx y 2 2xy dy 0 wesolvethem com completing the square example more complicated roots of polynomials using synthetic division completing the square with radical answer both values produce true statements therefore they are both solutions to the equation