Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 months ago

MATH QUESTION HELP!~?

State the discriminant of 6x^2 - 2x + k and state for which values of k would result in two different real solutions 

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  • 7 months ago
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    For a given quadratic expression of the form ax^2 + bx + c, the discriminant is given by b^2 - 4ac.

    In your case, we have:

    a = 6

    b = -2

    c = k

    Hence the discriminant is (-2)^2 - 4(6)(k) = 4 - 24k.

    Now there are three cases of solutions to the quadratic equation ax^2 + bx + c involving the discriminant, and this ties in with the quadratic formula which involves taking the square root of the discriminant in part of that formula

    Reminder: the quadratic formula is given by (-b ± √(b^2 - 4ac)) / 2a

    If the discriminant is positive, then there would be a real value for the square root of the discriminant (call that value p). Now the solutions would be:

    (-b + p) / 2a and (-b - p) / 2a.

    Note that there are two different solutions since we have plus and minus p.

    If the discriminant is equal to 0, then the square root of the discriminant is 0. Now the solutions would be:

    (-b ± 0) / 2a = -b / 2a.

    Note that there is only one unique solution in this case since we have plus and minus 0.

    If the discriminant is negative, then the square root of the discriminant is a complex number and no real solutions exist. You could express the roots of the equations as complex numbers. 

    Anyway, back to your question: to obtain two different real solutions, you need the case when the discriminant is greater than 0.

    Hence we have

    4 - 24k > 0

    -24k > -4...........subtracting 4 from both sides

    k < 4/24............dividing by -24 on both sides (note the sign change due to division by a negative number).

    Final answer: k < 1/6

  • 7 months ago

    the discriminant is B^2-4AC.......in your problem B = -2 and A = 6 and C=k so discriminant is 4-24k.........now there is a fact that you just have to memorize:  if the discriminant is positive, then there are two real solutions.     so set 4-24k to be greater than zero and solve for k......if k is less than 1/6, the discriminant is greater than 0.

    Final answer

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