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    1. Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer.

    a) x2 + 3x - 15 = 0
    b) x2 + x + 4 = 0
    c) x2 - 4x - 7 = 0
    d) x2 - 8x + 16 = 0
    e) 2x2 - 3x + 7 = 0
    f) x2 - 4x - 77 = 0
    g) 3x2 - 7x + 6 = 0
    h) 4x2 + 16x + 16 = 0

    2. Find an equation for which -3 and 4 are solutions.

    3. What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation.

    4. Create a real-life situation that fits into the equation (x + 3)(x - 5) = 0 and express the situation as the same equation.

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    Solution Preview

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    Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer.

    a) x^2 + 3x - 15 = 0

    Here a = 1, b = 3, c = -15

    We can find number/type of solutions by using discriminant:

    Discriminant D = b^2 - 4ac = 3^2 - 4*1*(-15) = 9 + 60 = 69

    Since D> 0, there will be "Two real solutions".

    b) x^2 + x + 4 = 0

    Here a = 1, b = 1, c = 4

    We can find number/type of solutions by using discriminant:

    Discriminant D = b^2 - 4ac = 1^2 - 4*1*4 = 1 - 16 = -15

    Since D< 0, there will be "Two Imaginary/complex solutions".

    c) x^2 - 4x - 7 = 0

    Here a = 1, b = -4, c = -7

    We can find number/type of solutions by using discriminant:

    Discriminant D = b^2 - 4ac = (-4)^2 - ...

    Solution Summary

    This solution helps go through various calculus problems using discriminants.

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