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The DISCRIMINANT is the part of the Quadratic formula under the radical The DISCRIMINANT tells you how many solutions (2, 1,or 0) A Quadratic Equation, like x2 + 5x + 4, has. The DISCRIMINANT is the part of the Quadratic formula under the radical √ √ √ Before working with the Quadratic Formula, let's look at how radicals behave. -9 9 0 = = = ERROR √ √ √ Before working with the Quadrartic Formula, let's look at how radicals behave. -9 9 0 = = = ERROR 0 3 Example: 3 x 3 = (not -9) (-3) x (-3) = (not -9) The square root of a negative number will be negative. Look at this example to see how ∓ shows up to 2 possible answers The plus/minus shows two possible answers 10 ∓ 10 ∓ √ 9 The discriminant equals b2 - 4ac The plus/minus shows two possible answers 10 + 3 = 10 ∓ 10 ∓ √ AND 3 9 The discriminant equals b2 - 4ac 10 - 3 = The plus/minus shows two possible answers 10 + 3 = 13 Solutions (roots) are 13 and 7. 10 ∓ 10 ∓ √ AND 3 9 The discriminant equals b2 - 4ac 10 - 3 = A positive discriminant (number under radical) gives 2 solutions 7 The plus/minus shows two possible answers 40 ∓ 40 ∓ √ 0 The discriminant equals b2 - 4ac The plus/minus shows two possible answers 40 + 0 = 40 ∓ 40 ∓ √ AND 0 0 The discriminant equals b2 - 4ac 40 - 0 = The plus/minus shows two possible answers 40 + 0 = 40 The solution (root) is 40 40 ∓ 40 ∓ √ AND 0 0 The discriminant equals b2 - 4ac 40 - 0 = A zero discriminant (number under radical) gives 1 solution 40 7 + 4 A positive discriminant, such as 16, would give you _____ real solutions. Example: 7 ∓ √16 7 - 4 solution (s) zero two one 7 + 0 A zero discriminant, (0), would give you _____ real solutions. Example: 7 ∓ √0 7 - 0 solution (s) zero two one 7 + imaginary number A negative discriminant, like -16, would give you _____ real solutions. Example: 7 ∓ √-16 7 - imaginary number solution (s) zero two one 7 + √5 A positive discriminant, such as 5, would give you _____ real solutions. Example: 7 ∓ √5 7 - √5 solution (s) zero two one Even though the √5 is not a perfect square, it will still give you two real solutions.
The solutions will be irrational (you can't get rid of the radical √ ) CLICK OK Negative radicals like √-7 and √-4 will give you real solution(s) Positive radicals like √9 and √5 will give you real solution(s) Zero radicals like √0 will give you real solution(s) 2 ? 0 ? 1 ? Place the correct number of solutions under each quadratic 1 Real Solution ? 2 RealSolutions ? No RealSolution ? ANSWERS ANSWERS ANSWERS 1 RealSolution 2 RealSolutions No RealSolution DISCRIMINANT PART I COMPLETE |