2x^3 - 5x^2 - 14x + 8
Let P(x) represents the cubic polynomial. We can find the sum of x-values which make P(x) = 0, (the sum of the roots of the equation)
P(x) = 2x^3 - 5x^2 - 14x + 8
P(x) = 0
2x^3 - 5x^2 - 14x + 8 = 0
Since the degree of this polynomial is odd, then the sum of the roots is -[a(n - 1)/an], where a(n-1) is -5 and an is 2. So we have,
-[a(n - 1)/an] = -(-5/2) = 5/2
Thus the sum of the roots is 5/2.
when the equation is equal to zero. . .:)
Multiply x3 - 2x2 - 13x - 10
take out zeros
a
(b+8)(b+8)
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.
when the equation is equal to zero. . .:)
To find the zeros of the polynomial from the given graph, identify the points where the graph intersects the x-axis. These intersection points represent the values of x for which the polynomial equals zero. If the graph crosses the x-axis at specific points, those x-values are the zeros of the polynomial. If the graph merely touches the x-axis without crossing, those points indicate repeated zeros.
by synthetic division and quadratic equation
Find All Possible Roots/Zeros Using the Rational Roots Test f(x)=x^4-81 ... If a polynomial function has integer coefficients, then every rational zero will ...
If there is one variable. Then put each variable equal to zero and then solve for the other variable.
Multiply x3 - 2x2 - 13x - 10
To find the quadratic polynomial whose zeros are 2 and -3, we can use the fact that a polynomial can be expressed in factored form as ( f(x) = a(x - r_1)(x - r_2) ), where ( r_1 ) and ( r_2 ) are the zeros. Here, substituting ( r_1 = 2 ) and ( r_2 = -3 ), we have ( f(x) = a(x - 2)(x + 3) ). Expanding this, we get ( f(x) = a(x^2 + x - 6) ). For simplicity, we can choose ( a = 1 ), giving us the polynomial ( f(x) = x^2 + x - 6 ).
In general, there is no simple method.
The function ( f(x) = x^2 - 6x + 8 ) is a polynomial function because it is a quadratic expression. To find the zeros, we can factor it as ( (x - 2)(x - 4) ), which gives us the zeros ( x = 2 ) and ( x = 4 ). Thus, the zeros of the function are 2 and 4.
To find the zeros of the polynomial function ( f(x) = x^3 - 2x^2 - 8x ), we first factor the expression. We can factor out ( x ) from the polynomial, giving us ( f(x) = x(x^2 - 2x - 8) ). Next, we can factor the quadratic ( x^2 - 2x - 8 ) into ( (x - 4)(x + 2) ), leading to ( f(x) = x(x - 4)(x + 2) ). Therefore, the zeros of the function are ( x = 0 ), ( x = 4 ), and ( x = -2 ).
If you have the zeros of a polynomial, it is easy, almost trivial, to find an expression with those zeros. I am not sure I understood the question correctly, but let's assume you have the zero 2 with multiplicity 2, and other zeros at 3 and 5. Just write the expression: (x-2)(x-2)(x-3)(x-5). (Example with a negative zero: if there is a zero at "-5", the factor becomes (x- -5) = (x + 5).) You can multiply this out to get the polynomial if you like. For example, if you multiply every term in the first factor with every term in the second factor, you get x2 -2x -2x + 4 = x2 -4x + 4. Next, multiply each term of this polynomial with each term of the next factor, etc.