SOLUTION: use factoring to solve the quadratic equation
x(x-2)^3 - 35(x-2)^2 =0
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Question 513731: use factoring to solve the quadratic equation
x(x-2)^3 - 35(x-2)^2 =0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It is not a quadratic equation. Quadratic equations have polynomials of degree 2. This equation has a polynomial (if you multiply it out) of degree 4. It is a quartic equation.
Be that as it may, since most of the difficult factoring work has been done, take two factors of )
out. The difference is that the end result will have four roots instead of just two (The Fundamental Theorem of Algebra said it, I believe it, that settles it)
^3\ -\ 35(x\ -\ 2)^2\ =\ 0)
^2\left(x(x\ -\ 2)\ -\ 35\right)\ =\ 0)
Get rid of the inner parentheses:
^2\left(x^2\ -\ 2x\ -\ 35\right)\ =\ 0)
You can see right away that two of your roots are 2 and 2. Use the fact that -7 plus 5 is -2 and -7 times 5 is -35 to factor the quadratic term, giving you 7 and -5 as the additional two roots.
John
My calculator said it, I believe it, that settles it
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