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# Mercy Young

### Module 17 - Solving Quadratic Equations by the Quadratic Formula

QuestionAnswer
What is the Quadratic Formula? A quadratic equation written in the form ax<sup>2</sup> + bx + c = 0 has the solutions: x=-b±√(b<sup>2</sup>-4ac)/2a
Use the Quadratic formula to solve:<br /> 2x=5x<sup>2</sup>-3 Answers are: -3/5, 1
Use the Quadratic formula to solve:<br /> y<sup>2</sup>+5y = -2 Answers are: -5-√(17)/2, -5+√(17)/2
Why does knowing the discriminant of a quadratic equation help in finding the solution? By knowing the discriminant, one can predict the possible outcomes of a quadratic equation. If the outcome of the radicand is: <br /> Positive = 2 real solutions.<br /> Zero = 1 real solution <br /> Negative = 2 complex but not real solutions.
Use the discriminant to determine the number and types of solutions to the equation:<br /> 4x<sup>2</sup>+12x=-9 The value of the radicand is Zero, so the equation has one real solution.
Use the discriminant to determine the number and types of solutions to the equation:<br /> 9y-2y<sup>2</sup>+5=0 The value of the radicand is positive, so the equation has two real solutions.
Solve:<br /> 2x = √(11x + 3) Answer = 3
Solve:<br /> 2x<sup>2/3</sup>+3x<sup>1/3</sup>-2=0 Answers are: 1/8, -8
Solve:<br /> 27x<sup>4</sup>+15x<sup>2</sup>=2 Answers are: -1/3, 1/3, -i√(6)/3, i√(6)/3
Use the Quadratic formula to solve:<br /> (m + 2)(2m - 6)= 5(m - 1) - 12 Answers are: 5/2, 1
Created by: MercyLaney