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The discriminant = b2 -4ac The DISCRIMINANT is the part of the Quadratic Formula under the √radical The DISCRIMINANT determines how many solutions the equation has.
The DISCRIMINANT also determines whether the solutions are:
rational (can be taken out of the radical) or
irrational (cannot be taken out of the radical) The DISCRIMINANT is the part of the Quadratic Formula under the √radical √9 = 3 √7 = √7 irrational ? rational ? The DISCRIMINANT determines how many solutions the equation has.
The DISCRIMINANT also determines whether the solutions are
(can be taken out of the radical) or
(cannot be taken out of the radical) The is the part of the Quadratic Formula under the √radical discriminant ? √9 = 3 √7 = √7 Negative radicals like √-7 and √-4 will give you real solution(s) Positive radicals like √9 and √5 will give you real solutions Zero radicals like √0 will give you real solution(s) 0 ? 2 ? 1 ? √ √ √ 64 PERFECT SQUARES are √radicals with WHOLE NUMBER (0,1,2,3,..) solutions 25 16 Simplify each perfect square below to a WHOLE number = = = 8 √ √ √ 4 9 100 = = = √ √ √ 121 PERFECT SQUARES are √radicals with WHOLE NUMBER (0,1,2,3,..) solutions 81 144 Simplify each perfect square below to a WHOLE number = = = 11 √ √ √ 36 49 1 = = = 20 +√7 These are the 2 irrational solutions
The seven cannot be taken out of the radical Imperfect positive radicals like √7 give 2 irrational solutions 20 ∓√7 Positive discriminants give 2 real solutions: 20 -√7 Perfect square positive radicals like √9 give 2 rational solutions 20 + 20 +√9 20 ∓√9 20 - 20 -√9 20 +√7 These are the 2 irrational solutions
The seven cannot be taken out of the radical Imperfect positive radicals like √7 give 2 irrational solutions 20 ∓√7 Positive discriminants give 2 real solutions: 20 -√7 Perfect square positive radicals like √9 give 2 rational solutions 20 + 3 20 +√9 20 ∓√9 20 -√9 20 - 3 two solutions These are the 2 irrational solutions
The seven cannot be taken out of the radical 20 +√7 irrational ? 20 ∓√7 Positive discriminants give 2 real solutions: 20 -√7 These are the 2 rational solutions √9 reduced to 3 two solutions 20 +√9 20 + 3 23 rational ? 20 ∓√9 20 -√9 20 - 3 17 Even though √7 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 Even though √7 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 √ ) √ √ 5 3 √ √ 17 10 These IMperfect squares will give you two real IRRATIONAL solutions.
You cannot get rid of the radicals 2 rational roots (no radicals) If the discriminant is a perfect square, then the quadratic will have how many roots (solutions)? 1 real root 2 irrational roots (with radicals) no real roots (imaginary roots) 8 ∓√25 Perfect Square Example: If the discriminant is +positive+, but NOT a perfect square, then the quadratic will have how many roots (solutions)? 2 rational roots (no radicals) 1 real root 2 irrational roots (with radicals) no real roots (imaginary roots) Imperfect Square Example: 8 ∓√23 2 rational roots (no radicals) 1 real root 2 irrational roots (with radicals) no real roots (imaginary roots) If the discriminant is ZERO, then the quadratic will have how many roots (solutions)? Zero Discriminant Example: 8 ∓√0 If the discriminant is +positive+, but NOT a perfect square, then the quadratic will have how many roots (solutions)? 2 rational roots (no radicals) 1 real root 2 irrational roots (with radicals) no real roots (imaginary roots) Imperfect Square Example: 8 ∓√13 2 rational roots (no radicals) 1 real root 2 irrational roots (with radicals) no real roots (imaginary roots) If the discriminant is --NEGATIVE--, then the quadratic will have how many roots (solutions)? NEGATIVE Discriminant Example: 8 ∓√-7 If the discriminant is a perfect square, then the quadratic will have how many roots (solutions)? 2 rational roots (no radicals) 1 real root 2 irrational roots (with radicals) no real roots (imaginary roots) 8 ∓√49 Perfect Square Example: √ √ √ The End |