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26 October, 16:30

A quadratic equation is shown below: 3x^2 - 15x + 20 = 0 Part A: Describe the solution (s) to the equation by just determining the radicand. Show your work. Part B: Solve 3x^2 + 5x - 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

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  1. 26 October, 16:58
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    These are two questions and two answers:

    Question 1:

    A quadratic equation is shown below: 3x^2 - 15x + 20 = 0 Part A: Describe the solution (s) to the equation by just determining the radicand. Show your work.

    Answer: The negative value of the radicand means that the equation does not have real solutions.

    Explanation:

    1) With radicand the statement means the disciminant of the quadratic function.

    2) The discriminant is: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation: ax² + bx + c

    3) Then, for 3x² - 15x + 20, a = 3, b = - 15, and c = 20

    and the discriminant (radicand) is: (-15) ² - 4 (3) (20) = 225 - 240 = - 15.

    4) The negative value of the radicand means that the equation does not have real solutions.

    Question 2:

    Part B: Solve 3x^2 + 5x - 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

    Answer: two solutions x = 1 and x = - 8/3x

    Explanation:

    1) I choose factoring (you may use the quadratic formula if you prefer)

    2) Factoring

    Given: 3x² + 5x - 8 = 0

    Make 5x = 8x - 3x: 3x² + 8x - 3x - 8 = 0

    Group: (3x² - 3x) + (8x - 8) = 0

    Common factors for each group: 3x (x - 1) + 8 (x - 1) = 0

    Coomon factor x - 1: (x - 1) (3x + 8) = 0

    The two solutions are for each factor equal to zero:

    x - 1 = 0 ⇒ x = 1

    3x + 8 = 0 ⇒ x = - 8/3

    Those are the two solutions. x = 1 and x = - 8/3
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