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    Im stuck on this economics entrance question, it says:
    How many real roots does the equation (x^4) - (4x^3)+(4x^2)-10=0 have?

    I tried differentiation but have no idea where to go from there.
    The options are 0,1,2,3,4(the answer is 2)
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    (Original post by bruh2132)
    Im stuck on this economics entrance question, it says:
    How many real roots does the equation (x^4) - (4x^3)+(4x^2)-10=0 have?

    I tried differentiation but have no idea where to go from there.
    The options are 0,1,2,3,4(the answer is 2)
    Also another question I'm struggling with says for
    what values of a does the quadratic ax^2+(a-2)x=2 have distinct real roots-

    I have found the discriminant equation and it only has one root so I put there are no values of a but the answers says a is not 2
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    you can look at it graphically:

    write it as

    (x2 + 2 )2 - 14 - 4x3 = 0




    (x2 + 2 )2 = 14 + 4x3

    the LHS is a U shape with y intercept ( 0,4 )

    the RHS is a cubic with a point of inflexion at ( 0, 14 )

    the curves intersect twice...
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    (Original post by the bear)
    you can look at it graphically:

    write it as

    (x2 + 2 )2 - 14 - 4x3 = 0




    (x2 + 2 )2 = 14 + 4x3

    the LHS is a U shape with y intercept ( 0,4 )

    the RHS is a cubic with a point of inflexion at ( 0, 14 )

    the curves intersect twice...
    Thank you, that helped loads
 
 
 

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