Q&A for How to Solve a Cubic Equation

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  • Question
    How do you solve a simple cubic equation?
    David Jia
    Math Tutor
    David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
    Math Tutor
    Expert Answer
    If you only have x³ in an equation, you can isolate it and find the cube root of both sides. This only works with really simple equations, though—factoring is the best way to solve more complex equations.
  • Question
    How would I solve xy+z+z^3=1?
    Community Answer
    That equation has numerous answers because you've got three variables. To get one answer for three variables you need three equations. One possible answer would be x=1, y=-1, z=1 => (1)(-1)+1+1^3=1.
  • Question
    The question is: if 3 consecutive even numbers are multiplied and the result would be 960. What are those numbers and how did you did with the step?
    Elvis Kiprotich
    Community Answer
    Solve the equation using the discriminant approach you will get three values of x. X=8, X=-7+(-1i)√71, X=-7+i√71. Easy from here, you pick the real value of x, that's 8 and your three numbers were 8, 10 and 12.
  • Question
    Can you give a particular formula for solving cubic equations?
    Community Answer
    Yes, but it's highly impractical to memorize or even use: http://www.math.vanderbilt.edu/~schectex/courses/cubic/
  • Question
    How can there be a square root of -3?
    Donagan
    Top Answerer
    In the ordinary sense, there is no such thing as the square root of a negative number. However, mathematicians have invented the "imaginary" number known as "i", which is defined as the square root of negative 1. The square root of -3 is equal to "i" multiplied by the square root of 3, or 1.73 i.
  • Question
    What's the product of Alpha Beta Gamma Delta if they are the roots of the polynomial?
    Hemant Dikshit
    Community Answer
    It is the constant term of the polynomial. This is because Minus Alpha x Minus Beta x Minus Gamma x Minus Delta = Plus Alpha Beta Gamma Delta.
  • Question
    The link you gave above for a particular formula for solving cubic equations only seems to give one solution; how does one use that formula to get all 3 potential solutions?
    Eric Shen
    Community Answer
    By the Fundamental Theorem of Algebra, we have ax^3 + bx^2 + cx + d, which can be expressed as a(x-r)(x-s)(x-t). WLOG let the equation give r. Then, simply divide the cubic by (x-r) and we get a quadratic whose roots are the remaining two roots.
  • Question
    What is the solution to 6y3 + 4y2 -5y = 2?
    ayodeji oyenaike
    Community Answer
    Multiply and collect: 6y3 + 4y2 - 5y = 2, therefore 21y = 2. The answer is y = 2 / 21.
  • Question
    Can anyone factorize x^3+4x-2?
    Community Answer
    Yes. It is possible. All you need to do is use the factoring approach, only first you must add 2 to both sides. After, you can factor it to (x) (x^2 + 4) = 2. Divide both sides by x to get x^2 + 4 = 2/x. Subtract 4 from both sides to get x^2 = 2/x - 4. Square root both sides to get x = ±√(2x - 4).
  • Question
    If N3+N=2x, how do I find N?
    Community Answer
    First simplify the equation to 4N = 2x. Then divide each side by 4 to get N = (2x)/(4).
  • Question
    How to solve A^3 -A = 60?
    Community Answer
    Before trying advanced methods like the cubic formula, do a quick check for rational roots -- you might get lucky. Here the Rational Roots Theorem implies than any rational roots must be integer divisors of 60. A little trial and error then reveals 4^3 - 4 = 64-4 = 60, so A=4 is a solution. If you require all real and complex solutions, use the known solution to factor A^3 - A - 60 = (A-4)(A^2 + 4A + 15). The quadratic factor has no real roots, but its two complex solutions can be found via the quadratic formula.
  • Question
    How to solve this equation: 3x^3+7x^2-4=0?
    Harshit Aseeja
    Community Answer
    Find the prime factors of 3 and -4 and divide each factor of -4 by each factor of 3, you will get a set of 12 numbers. you need to plug in these 12 numbers in your cubic equation, and whichever of them yields 0, is your answer. Here the answer is x= -1, -2 and (2/3).
  • Question
    How to solve x^3-4x-3=0?
    Harshit Aseeja
    Community Answer
    Find factors of 1 (coefficient of x cube) and factors of -3 (constant term) then divide the factors of -3 by the factors of 1. You will get a set of 4 numbers. plug in these 4 numbers in your cubic equation and 3 of them will yield 0 which will be your solutions for x.
  • Question
    How do you find a maxima and minima of a cubic function?
    Jasmine Snowdrop
    Community Answer
    Differentiate the equation and equate the derivative to zero. Solve for the variable and you will get values of x at which the derivative is zero. Use those values to find the corresponding values of y and the points you obtain will be the points of inflection. Do the second derivative test, and the points at which the second derivative is positive, the function has local minima, and the points at which the second derivative is negative, the function has local maxima.
  • Question
    I want to find the value of p in the following equation: 3 x 3 + (p + 3) x 2 + (7 - p - 4p2) x - 4 = 0. How can I do it?
    Community Answer
    This is not a cubic. Anyway, always simplify noting that there is no simple term or factor that can be taken out first (e.g. p+3 etc). So 9 + 2p+6 -28 +4p +16p^2 = 0 -13 +6p +16p^2 = 0 16p^2 + 6p -13 = 0 Solve from here.
  • Question
    What is an example of a quadratic equation?
    Donagan
    Top Answerer
    A quadratic equation can be expressed in the standard form ax² + bx + c = 0, where a does not equal zero. (This form can be thought of as +/- ax² +/- bx +/- c = 0.) Examples include 3x² + 2x + 5 = 0, and x² - x - 1 = 0.
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