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Math Help - need help fotr math

  1. #1
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    need help fotr math

    Quote Originally Posted by Bajan View Post
    Hey guys, having trouble with this problem :-/
    how to find a quadratic equation is standard from whoes rooot are given by

    r₁=3+√2 and r₂=3-[FONT='Arial','sans-serif']√2
    [/FONT]
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    Quote Originally Posted by tejashtaj View Post
    how to find a quadratic equation is standard from whoes rooot are given by

    r₁=3+√2 and r₂=3-[FONT='Arial','sans-serif']√2[/font]
    You know the values of the two roots, and we know that one form of the quadratic for this will be given by
    (x - r_1)(x - r_2)

    Thus
    (x - (3 + \sqrt{2} ))(x - (3 - \sqrt{2}))

    The simplest way to expand this (in my opinion) is to write this as
    ((x - 3) - \sqrt{2} ) ((x - 3) + \sqrt{2})
    which is in the form of (a - b)(a + b) = a^2 - b^2,

    ((x - 3) - \sqrt{2} ) ((x - 3) + \sqrt{2}) = (x - 3)^2 - (\sqrt{2})^2

    = x^2 - 6x + 9 - 2 = x^2 - 6x + 7
    as you can check.

    -Dan
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    write a quadratic of the form f(x)=a[FONT='Arial','sans-serif']x +bx +c for the quadratic function whose graph passes through the point (o,8),(8,0) and (-2,5).[/FONT]

    [FONT='Arial','sans-serif'](Hint find the values of a,b and c!)[/FONT]
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    Quote Originally Posted by tejashtaj View Post
    write a quadratic of the form f(x)=a[FONT='Arial','sans-serif']x +bx +c for the quadratic function whose graph passes through the point (o,8),(8,0) and (-2,5).[/font]

    [FONT='Arial','sans-serif'](Hint find the values of a,b and c!)[/font]
    Substitute the given values into the general equation, and you will end up with a system of linear equations in a,\;b,\text{ and }c:

    \begin{array}{rcl}<br />
(x,\;y) &\rightarrow& y = ax^2 + bx + c\\<br />
(0,\;8) &\rightarrow& 8 = a(0)^2 + b(0) + c\\<br />
(8,\;0) &\rightarrow& 0 = a(8)^2 + b(8) + c\\<br />
(-2,\;5) &\rightarrow& 5 = a(-2)^2 + b(-2) + c<br />
\end{array}

    and you get the following system:

    \left\{\begin{array}{rcrcrcr}<br />
64a & + & 8b & + & c & = & 0\\<br />
4a & - & 2b & + & c & = & 5\\<br />
&&&& c & = & 8<br />
\end{array}\right.

    Now solve for the needed coefficients.
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