Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

what are the solutions to the equation: Y=x3+3x2-4x-12?

A:2, -2,3

B:-2,2,-3

C:3,4

D:3,4,12

9 Answers

Relevance
  • gare
    Lv 5
    1 decade ago
    Favorite Answer

    Are A-D our only choices? The actual "solutions" are infinite, in that there is no solution. x may equal any number and by assigning a number to x you get a number for Y. Or, conversely, y may equal any number and you must solve for x. There are an inifinite number of numbers we may assign to X or Y. Using Y as the example, if it is with Y=0, then they do not even need the Y it should just read x^3 + 3x^2 -4x -12 = 0, then we may solve for all values of x relative to one specific answer. Then the question makes sense to select from the answers provided because we are merely looking for the solutions or roots which are exactly the x-intercepts of the function.

    Example(s): let y = 0 and solve the problem. Then the (b) answer works. However:

    Let y=1, let y = -1, let y = 2, etc. None of the answers now work but it is still an equation that will have a solution.

  • 1 decade ago

    Ok, y=(x^3)+3(x^2)-4x-12. For solutions I take it you mean the roots of this equation, i.e. values of x for which y=0. Since y is a tri-nomial (x^3 being the highest power) we can expect at most 3 unique roots.

    Let's regroup the right hand side to see if we can simplify it a bit.

    Y=x3-4x+3x2-12

    Y=x(x2-4)+3(x2-4)

    Y=(x+3)(x2-4)

    Y=(x+3)(x+2)(x-2)

    so setting y=0 we indeed get three roots for x, as expected, and they are x=-3, x=+2, and x=-2 so the answer is B

    We got lucky in that we could simplify this, you may not always be able to do this! Whether you can simplify it or not to easily pick out the roots, you can always graph the function and see where it crosses the y axis, or where y=0. Hope this helps!

  • 1 decade ago

    I'm assuming that by solution, you mean roots. Then the answer is B. You factor x^3+3x^2-4x-12

    =x^2(x+3)-4(x+3)

    =(x^2-4)(x+3)

    =(x-2)(x+2)(x+3)

    Setting this equal to zero gives you the solutions x=2,-2,-3

  • 1 decade ago

    Factor by (re)grouping.

    y=x³ + 3x² - 4x - 12

    y= (x³ + 3x²) + (-4x - 12), factor out GCFs from each group

    y=x²(x + 3) - 4(x + 3), rewrite/regroup x² & -4 as a binomial factor of the binomial (x+3)

    y=(x² - 4)(x + 3) factor (x² - 4) further..

    y=(x + 2)(x - 2)(x + 3), set each binomial equal to zero.

    (x+2)=0 or (x-2)=0 or (x+3)=0, solve each for x

    x = -2 or x = 2 or x = -3

    The answer is B.

  • How do you think about the answers? You can sign in to vote the answer.
  • Erika
    Lv 4
    5 years ago

    ?3/(?(9+y^2 ))dy=?4xdx ----- (a million) combine the left edge enable y = 3 sinh(t) dy=3 cosh(t) dt 9+y^2=9+9 sinh^2(t) = 9(a million+sinh^2 (t)) = 9 cosh^2(t) sqrt(9+y^2)=sqrt(cosh^2(t)) = 3 cosh(t) ?3/(?(9+y^2 ))dy = ? 3 [3 cosh(t) dt] / 3cosh(t) = 3 ? dt = 3 t+C = 3 sinh^-a million(y/3) ?4xdx = 2x^2 (a million) turns into: 3 sinh^-a million(y/3) = 2x^2 + C sinh^-a million(y/3) = (a million/3) {2x^2+C] y/3 = sinh[ (a million/3) (2x^2 + C)] y = 3 sinh[ (a million/3) (2x^2 + C)] it quite is the prevalent answer

  • Anonymous
    1 decade ago

    my answer is B:-2,2,-3.....b'coz when substituting these 3 values in the equation we get Y=0..

  • 1 decade ago

    The answer to your question simply the letter B

    the solutions are:

    -3, -2, 2

    Try to use the link below in solving any math problems.

    i got it from WAL.

    by the way thanks WAL. I learned something from you.

  • 1 decade ago

    I am only in Algebra, and the reason why I am typing this is because I need more points=)

  • 1 decade ago

    B

Still have questions? Get your answers by asking now.