Page 1 of 2 12 LastLast
Results 1 to 15 of 25

Math Help - Factoring a quadratic equation

  1. #1
    Senior Member
    Joined
    Jul 2008
    Posts
    313

    Factoring a quadratic equation

    I have a quadratic equation;

    3x^2 - 2x +3

    I am asked to calaculate the discriminate of the quadratic expression

    OK this is a learning curve for me which I don't profess to understand!

    I have the above and I think the first step is to find the sum of the two numbers 'a' and 'c', so ac = 9. The sum is b

    for this quadratic expression, ac = 3 x 3 = 9 and b = -2

    I think I now need to find the factors of 9!

    I see 1, 3 and 9

    The problem I now see is there is no sum of these to make -2, so I am stuck here at this point?

    Anyone know what I am doing wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Factoring a quadratic equation

    Do you know the discriminant is:
    D=b^2-4ac
    ?
    You have: a,b and c so you can calculate it directly.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1478
    Awards
    1

    Re: Factoring a quadratic equation

    Quote Originally Posted by David Green View Post
    I have a quadratic equation;
    3x^2 - 2x +3
    to calaculate the discriminate of the quadratic expression
    \Delta=b^2-4ac is the discriminate.

    b=-2,~a=3,~\&~c=3 so \Delta=(-2)^2-4(3)(3)=-32
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jul 2008
    Posts
    313

    Re: Factoring a quadratic equation

    Quote Originally Posted by Siron View Post
    Do you know the discriminant is:
    D=b^2-4ac
    ?
    You have: a,b and c so you can calculate it directly.
    How does - 49 sound?

    I didn't know D = b^2 - 4ac, although it does look very similar to the quadratic equation b sqrt b^2 -4ac /2a
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1478
    Awards
    1

    Re: Factoring a quadratic equation

    Quote Originally Posted by David Green View Post
    How does - 49 sound?

    I didn't know D = b^2 - 4ac, although it does look very similar to the quadratic equation b sqrt b^2 -4ac /2a
    Read reply #3 carefully. It is correct. The answer is -32
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Jul 2008
    Posts
    313

    Re: Factoring a quadratic equation

    Quote Originally Posted by Plato View Post
    Read reply #3 carefully. It is correct. The answer is -32
    Thanks all for your help, I just worked it out. b^2 first, the - 2 becomes a positive when squared, then the product rule, then subtract from the squared value to = - 32.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Factoring a quadratic equation

    Maybe something important, if D<0, do you know what that means? Does the parabola intersect the x-axis in certain point(s)? ...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Jul 2008
    Posts
    313

    Re: Factoring a quadratic equation

    Quote Originally Posted by Siron View Post
    Maybe something important, if D<0, do you know what that means? Does the parabola intersect the x-axis in certain point(s)? ...
    I might be wrong but it could be referring to a negative solution?

    On this example; x^2 + x - 12 = 0

    can I use the quadratic formula?

    If so is it only the integers on the top line under the square root that should be square rooted, then divide then either add or subract the remaining b?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Factoring a quadratic equation

    Quote Originally Posted by David Green View Post
    I might be wrong but it could be referring to a negative solution?

    On this example; x^2 + x - 12 = 0

    can I use the quadratic formula?

    If so is it only the integers on the top line under the square root that should be square rooted, then divide then either add or subract the remaining b?
    Yes, you can use the quadratic formula for every quadratic equation.
    Now, it can be also important to know why you're calculating the discriminant. Probably you'll lear more about that.
    But if you calculate: 0=ax^2+bx+c which can be solved with the quadratic formula, you're calculing the point(s) where the parabola intersects the x-axis, because there y=0, now you can distinguish tree cases:
    - D<0, the parabola doesn't intersects the x-axis at all, so there are no intersect points and so no solution.
    - D=0, there parabola intersects the x-axis, there are two equal solutions.
    - D>0, the parabola intersects the x-axis, there are two different intersect points and so two different solutions.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member
    Joined
    Jul 2008
    Posts
    313

    Re: Factoring a quadratic equation

    Quote Originally Posted by Siron View Post
    Yes, you can use the quadratic formula for every quadratic equation.
    Now, it can be also important to know why you're calculating the discriminant. Probably you'll lear more about that.
    But if you calculate: 0=ax^2+bx+c which can be solved with the quadratic formula, you're calculing the point(s) where the parabola intersects the x-axis, because there y=0, now you can distinguish tree cases:
    - D<0, the parabola doesn't intersects the x-axis at all, so there are no intersect points and so no solution.
    - D=0, there parabola intersects the x-axis, there are two equal solutions.
    - D>0, the parabola intersects the x-axis, there are two different intersect points and so two different solutions.
    Interesting stuff which I am learning, I have worked out that I have I think two routes, the positive route being 3 using the equation.

    This is what I did;

    -1 + or - square root 1^2 - 4 x 1 - 12
    2 x 1

    = 3

    Hope I got that right?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Factoring a quadratic equation

    You have found one solution, because D>0, there are two different solutions.
    You have found:
    x_1=\frac{-1+\sqrt{D}}{2}=3
    x_2=\frac{-1-\sqrt{D}}{2}=...?
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Senior Member
    Joined
    Jul 2008
    Posts
    313

    Re: Factoring a quadratic equation

    Quote Originally Posted by Siron View Post
    You have found one solution, because D>0, there are two different solutions.
    You have found:
    x_1=\frac{-1+\sqrt{D}}{2}=3
    x_2=\frac{-1-\sqrt{D}}{2}=...?
    There are two solutions, one positive and one negative, I only required the positive one on this example. Thanks David
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Factoring a quadratic equation

    Quote Originally Posted by David Green View Post
    There are two solutions, one positive and one negative, I only required the positive one on this example. Thanks David
    Fine!
    But why do you need only the positive solution?
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Senior Member
    Joined
    Jul 2008
    Posts
    313

    Re: Factoring a quadratic equation

    Quote Originally Posted by Siron View Post
    Fine!
    But why do you need only the positive solution?
    in the activity in question it only asked for the positive route, thanks David
    Follow Math Help Forum on Facebook and Google+

  15. #15
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Factoring a quadratic equation

    Ok, then what you wright is good enough.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 29th 2011, 12:08 PM
  2. factoring a basic quadratic equation
    Posted in the Algebra Forum
    Replies: 7
    Last Post: May 10th 2011, 09:00 PM
  3. quadratic equation by factoring
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 6th 2010, 10:24 PM
  4. Factoring Quadratic Equation?
    Posted in the Algebra Forum
    Replies: 6
    Last Post: June 20th 2009, 05:59 PM
  5. Factoring a quadratic equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 15th 2009, 06:52 AM

Search Tags


/mathhelpforum @mathhelpforum