6ExampleSolve the equation 3x2 − 6x + 3 = 0. Support your result graphically. Solution Let a = 3, b = −6 and c = 3.
7ExampleSolve the equation 2x2 + 4x + 5 = 0. Support your result graphically. Solution Let a = 2, b = 4 and c = 5.There are no real solutionsfor this equation becauseis not a real number.
8THE DISCRIMINANT AND QUADRATIC EQUATIONSTo determine the number of solutions to the quadratic equation ax2 + bx + c = 0, evaluate the discriminant b2 – 4ac.1. If b2 – 4ac > 0, there are two real solutions.2. If b2 – 4ac = 0, there is one real solution.3. If b2 – 4ac < 0, there are no real solutions; there are two complex solutions.
9ExampleUse the discriminant to determine the number of solutions to −2x2 + 5x = 3. Then solve the equation using the quadratic formula. Solution −2x2 + 5x − 3 = 0 Let a = −2, b = 5 and c = −3.b2 – 4ac= (5)2 – 4(−2)(−3)= 1orThus, there are two solutions.
10THE EQUATION x2 + k = 0If k > 0, the solution to x2 + k = 0 are given by