Let's say y1, y2, and y3 are zeros. Set up an expression like this (x-y1)(x-y2)(x-y3) [This is factored form] and then multiply carefully. That works with any number of roots. If 0 is a root, add an x by itself to the beginning of the factored form expression. Also, imaginary roots come in twos. Therefore, if given i as a root, you need (x-i)(x+i). If you have something in x + yi form for a root, you'll need the complex conjugate. That would make (x-(a+bi))(x-(a-bi))
If the cubic polynomial you are given does not have an obvious factorization, then you must use synthetic division. I'm sure wikipedia can tell you all about that.
You solve the equation.
To find the possible rational zeros of the polynomial ( f(x) = x^3 + 8x + 6 ), we can use the Rational Root Theorem. The possible rational zeros are given by the factors of the constant term (6) over the factors of the leading coefficient (1). Therefore, the possible rational zeros are ( \pm 1, \pm 2, \pm 3, \pm 6 ).
(1,2) (0,5) (-1,8) (2,-1) (-2,11) All of these are solutions to the given equation.
Ah, don't you worry, friend. In a Mega Millions jackpot, there are quite a few zeros! You'll find six zeros in a million and nine zeros in a billion. Just imagine all the happy little zeros lining up to bring joy and excitement to someone's life.
If the cubic polynomial you are given does not have an obvious factorization, then you must use synthetic division. I'm sure wikipedia can tell you all about that.
They are all the points where the graph crosses (or touches) the x-axis.
You could try setting the function equal to zero, and finding all the solutions of the equation. Just a suggestion.
You solve the equation.
The solution set for a given equation is the set of all points such that their coordinates satisfy the equation.
is a set of all replacements that make an equation time in mathematics solution set is set of values which satisfies a given equation. For solving solutions you can get help from online Find Math Solutions.
To find the possible rational zeros of the polynomial ( f(x) = x^3 + 8x + 6 ), we can use the Rational Root Theorem. The possible rational zeros are given by the factors of the constant term (6) over the factors of the leading coefficient (1). Therefore, the possible rational zeros are ( \pm 1, \pm 2, \pm 3, \pm 6 ).
(1,2) (0,5) (-1,8) (2,-1) (-2,11) All of these are solutions to the given equation.
Ah, don't you worry, friend. In a Mega Millions jackpot, there are quite a few zeros! You'll find six zeros in a million and nine zeros in a billion. Just imagine all the happy little zeros lining up to bring joy and excitement to someone's life.
They are -1, 1 and 5.
yes. technically all decimals have an infinite amount of zeros behind them. you just have to apply significant digits to find how much zeros you are suppose to write.
x = -1.2153 x = 2.0614