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Thread: quadratic equation

  1. #1
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    quadratic equation

    What the terms to quadratic question in math?
    What the terms to quadratic equation?
    How I know that the equation is quadratic?
    What are the ways to turn an equation (that not quadratic or not seen quadratic) to quadratic?
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  2. #2
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    Re: quadratic equation

    The term "quadratic" refers to the second power. A "quadratic equation" is a polynomial equation in which the unknown appears to the second power but no higher power. Any quadratic equation can be written in the form "$\displaystyle ax^2+ bx+ c= 0$" where "x" is the unknown and "a", "b", and "c" are constants. It is fairly basic algebra to show that any quadratic has two (complex number) solutions given by the formula $\displaystyle x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}$ where one solution is given by the "+" and the other by the "-". The two solutions will be real numbers if and only if $\displaystyle b^2- 4ac\ge 0$.

    There are no general methods for changing a non-quadratic equation into a quadratic equation but there are some equations that can- sometimes called "of quadratic type". For example, the equation $\displaystyle x^6- 5x^3+ 6= 0$, while it is of 6th degree, is "of quadratic type" because the substitution $\displaystyle y= x^3$ changes it to $\displaystyle y^2- 5y+ 6= 0$. That can be factored as $\displaystyle (y- 3)(y- 2)= 0$ so (because if ab= 0 then either a or b must be 0) either y- 3= 0 or y- 2= 0 so that y= 3 or y= 2. Of course, we have not yet solved the original equation. Since $\displaystyle y= x^3$, we still must solve $\displaystyle x^3= 3$ and $\displaystyle x^3= 2$. Those will each have three complex solution so the original equation has 6 solutions, two real and the other four non-real.
    Last edited by HallsofIvy; Jul 16th 2018 at 04:16 AM.
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  3. #3
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    Re: quadratic equation

    Quote Originally Posted by yyakob View Post
    What the terms to quadratic question in math?
    What the terms to quadratic equation?
    How I know that the equation is quadratic?
    What are the ways to turn an equation (that not quadratic or not seen quadratic) to quadratic?
    Did your math teacher not explain all that?
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