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Math Help - Form (x + a)^2 +b

  1. #1
    Junior Member Mist's Avatar
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    Discriminant

    What does the term 'Discriminant' mean?

    The question is: Calculate the Discriminant of  3x^2 + 5x +8
    Last edited by Mist; October 26th 2009 at 01:40 AM.
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  2. #2
    Member rowe's Avatar
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    The discriminant of a polynomial of the form ax^2 + bx + c, is b^2 -4ac. The discriminant is an important feature which, among other things, helps us to determine the nature of the roots of the polynomial.

    In your case, you have 3x^2 + 5x + 8, so the discriminant will be 5^2- 4 \cdot 3 \cdot 8 = 25 - 96 = -71.
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  3. #3
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    Recall that the solutions to the quadratic equation ax^2+ bx+ c= 0 are, by the quadratic formula, \frac{-b\pm\sqrt{b^2- 4ac}}{2a}. Whether there are two real roots, one double root, or two complex roots depends upon whether the number in the square root, b^2- 4ac is positive, zero, or negative.

    That number, b^2- 4ac is the "discriminant".

    As row said, in your case, the discriminant is -71. That tells us that the equation 3x^2+ 5x+ 8= 0 has two complex roots.

    It als tells us that the graph of y= 3x^2+ 5x+ 8 does not cross the x-axis but is entirely in the upper half-plane.
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  4. #4
    Junior Member Mist's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    Recall that the solutions to the quadratic equation ax^2+ bx+ c= 0 are, by the quadratic formula, \frac{-b\pm\sqrt{b^2- 4ac}}{2a}. Whether there are two real roots, one double root, or two complex roots depends upon whether the number in the square root, b^2- 4ac is positive, zero, or negative.

    That number, b^2- 4ac is the "discriminant".

    As row said, in your case, the discriminant is -71. That tells us that the equation 3x^2+ 5x+ 8= 0 has two complex roots.

    It als tells us that the graph of y= 3x^2+ 5x+ 8 does not cross the x-axis but is entirely in the upper half-plane.
    So, how do you find the intersection of the curve?
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  5. #5
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    Quote Originally Posted by Mist View Post
    So, how do you find the intersection of the curve?
    Intersection of the curve with what (note that you've been told in post #3 that it does NOT intersect the x-axis ....)
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