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Math Help - solve for k

  1. #1
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    Talking solve for k

    i don't know how to solve this, any help is appreciated.

    1. find the values of k such that 3x^2+kx+11=0

    2. find the value of so that the equation 6x^2-(k+4)x-9=8x has roots that are numerically equal but opposite in sign.

    thank you so much.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by princess_21 View Post
    i don't know how to solve this, any help is appreciated.

    1. find the values of k such that 3x^2+kx+11=0

    2. find the value of so that the equation 6x^2-(k+4)x-9=8x has roots that are numerically equal but opposite in sign.

    thank you so much.
    For quadratic equation
    ax^2 + bx +c =0

    1. Is it the exact question, anything about x ?? is it variable?

    For having real roots what's the condition??
    ....
    b^2 >4ac

    2. sum of roots of a quadratic is -b/a
    In our case -b/a= 0 ,

    so -k-4 -8= 0 ,solve!!
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  3. #3
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    Hello, princess_21!

    Another approach to #2 . . .


    2. Find the value of k so that the equation 6x^2-(k+4)x-9\:=\:8x
    has roots that are numerically equal but opposite in sign.
    The equation simplifies to: . 6x^2 - (k+12)x - 9 \:=\:0


    Consider the Quadratic Formula: . x \;=\;\frac{-b \pm\sqrt{b^2-4ac}}{2a}

    . . The roots will be equal and opposite in sign when b = 0.


    Hence: . -(k+12) \:=\:0 \quad\Rightarrow\quad\boxed{ k \:=\:\text{-}\,12}

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  4. #4
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    Quote Originally Posted by ADARSH View Post
    For quadratic equation
    ax^2 + bx +c =0

    1. Is it the exact question, anything about x ?? is it variable?

    For having real roots what's the condition??

    ....
    b^2 >4ac

    2. sum of roots of a quadratic is -b/a
    In our case -b/a= 0 ,

    so -k-4 -8= 0 ,solve!!
    this is the exact question..
    1. the values of k such that 3x^2+kx+11=0 has a unique real solution are _____ and _______.

    thanks for your time.
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by princess_21 View Post
    this is the exact question..
    1. the values of k such that 3x^2+kx+11=0 has a unique real solution are _____ and _______.

    thanks for your time.

    For having a single(real) root , we must have both the roots equal

    So as the given roots by Soroban




    Both the roots will be equal if

    b^2 = 4ac

    Put that thing in your equation

    So
    k^2 = 4*3 * 11

    k = \pm\sqrt{4*3*11}
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