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College Algebra--Still Confused

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I have a few problems I need help with and also do have multiple choice. If I can have an explanation of how to get the answer that would be great.

1. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.
x^2-4x=5
a.) Two rational roots
b.) one repreated root
c.) two complex roots
d.) two irrational roots.

2.Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.
-3x^3+19x-20=0
a.) Two rational roots
b.) one repreated root
c.) two complex roots
d.) two irrational roots.

3. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.
-5x^2-7x-5=0
a.) Two rational roots
b.) one repreated root
c.) two complex roots
d.) two irrational roots.

4. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots
x^2-12=7x
a.) Two rational roots
b.) one repreated root
c.) two complex roots
d.) two irrational roots.

  • College Algebra--Still Confused - ,

    In google type:

    quadratic equation online

    When you see list of result click on:

    Free Online Quadratic Equation Solver:Solve by Quadratic Formula

    When page be open in rectangle type your equation

    and cilck option:

    solve it!

    You will see solutions step-by step and discriminant discusion.

  • College Algebra--Still Confused - ,

    I am only going to do one,

    1. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.
    x^2-4x=5
    a.) Two rational roots
    b.) one repreated root
    c.) two complex roots
    d.) two irrational roots.
    ----------------
    Write with a zero on the right in form
    a x^2 + b x + c = 0
    1 x^2 -4 x - 5 = 0
    b^2 = (-4)(-4) = 16
    -4ac = -4(1)(-5) = +20
    so
    b^2 -4ac = 16+20 = 36
    sqrt (b^2 - 4ac) = +6
    THAT means:
    x = [ 4 +/- 6 ] /2
    Two REAL Rational roots
    BECAUSE
    sqrt (+36) is a real number
    sqrt (+36) is not sqrt( 0) which would give one repeated root
    sqrt(+36) is not sqrt(-36) which would leave you with a +/- 6i which is COMPLEX number
    it is not sqrt (2) or something which is not a nice rational number and can not be expressed as a ratio of whole numebers

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