Algebra

How many real number solutions does the equation have? 0 = -7x^2 + 6x + 3
one solution
two solutions**
no solution

How many real number solutions does the equation have? 0 = 2x^2 - 20x + 50
one solution
two solutions
no solution**

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  1. #1 ok
    #2 nope. the polynomial is 2(x-5)^2
    always check the discriminant. For this one, it is zero, indicating one repeated root.

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  2. Find the discriminant: D=b^2-4ac

    if D>0, there are two real number solutions
    if D=0, there is one solution
    if D<0, there are no solutions

    Using the quadratic equation: ax^2 + bx +c, insert the values into the discriminant.

    1) -7x^2 + 6x + 3

    D=(6)^2 - 4(-7)(3)
    =36+84
    =120>0
    Therefore, there are 2 real number solutions.

    2) 2x^2 - 20x + 50

    D=400-400
    = 0
    Therefore, there is one solution.

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  3. For the second one I thought it was negative?
    (-20)^2 - 4(2)(50) =
    - 400 - 400 = -800?

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  4. sorry ... b^2 = (-20)^2 = (-20)(-20) = 400 not -400
    -400 is -20^2 = -b^2 because exponents are done first.

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  5. thanks soo much everyone!! :3

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