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What kind of polynomial is 3x2y3?
If you mean: 3x+2y = 3 then it is a straight line equation
What is the difference between a polynomial and an equation?
Equations will have an equals sign. Such as: x + 3 = 2 Polynomials will not. Such as: 2x + 3
What are the solutions of the equation x3 plus 3x2-x-3 equals 0?
the solutions to this equation are -1,+1 and -3. you can solve this equation by using the polynomial long division method. we basically want to factorize this and polynomial and equate its factors to zero and obtain the roots of the equation. By hit and trial , it clear that x=1 i.e is a root of this equation. So (x-1) should be a factor of the given polynomial (LHS). Divide the polynomial by x-1 using long division method and you will get the quotient as x2+4x+3 and remainder would be 0 ( it should be 0 as we are dividing the polynomial with its factor. Eg when 8 is divided by any of its factor like 4,2 .. remainder is always zero ) Now, we can write the given polynomial as product of its factors as x3+3x2-x-3 = (x-1)(x2+4x+3) =(x-1)(x+1)(x+3) [by splitting middle term method] so the solutions for the given polynomial are obtained when RHS = 0, Hence x=-1 , X = +1, x=-3 are the solutions for this equation.
How do you determine the degrees of a given polynomial?
The degree of a polynomial is the highest power that appears in the polynomial. For more than one variable, you must add the powers for each variable, for example, a3b2 is of degree 3 + 2 = 5.
What is 5x cube -45x?
y = 5x^3 - 45x is a polynomial equation that crosses the y axis at x=3.
What is a polynomial of 3 items?
An example of a polynomial with 3 terms is 3x3 + 4x + 20, because there are 3 different degrees of x in the polynomial.
What kind of polynomial is 3x2y3?
If you mean: 3x+2y = 3 then it is a straight line equation
What is the difference between a polynomial and an equation?
Equations will have an equals sign. Such as: x + 3 = 2 Polynomials will not. Such as: 2x + 3
What are the solutions of the equation x3 plus 3x2-x-3 equals 0?
the solutions to this equation are -1,+1 and -3. you can solve this equation by using the polynomial long division method. we basically want to factorize this and polynomial and equate its factors to zero and obtain the roots of the equation. By hit and trial , it clear that x=1 i.e is a root of this equation. So (x-1) should be a factor of the given polynomial (LHS). Divide the polynomial by x-1 using long division method and you will get the quotient as x2+4x+3 and remainder would be 0 ( it should be 0 as we are dividing the polynomial with its factor. Eg when 8 is divided by any of its factor like 4,2 .. remainder is always zero ) Now, we can write the given polynomial as product of its factors as x3+3x2-x-3 = (x-1)(x2+4x+3) =(x-1)(x+1)(x+3) [by splitting middle term method] so the solutions for the given polynomial are obtained when RHS = 0, Hence x=-1 , X = +1, x=-3 are the solutions for this equation.
Is a polynomial with square root a polynomial?
It is a polynomial if the square root is in a coefficient but not if it is applied to the variable. A polynomial can have only integer powers of the variable. Thus: sqrt(2)*x3 + 4*x + 3 is a polynomial expression but 2*x3 + 4*sqrt(x) + 3 is not.
How do you determine the degrees of a given polynomial?
The degree of a polynomial is the highest power that appears in the polynomial. For more than one variable, you must add the powers for each variable, for example, a3b2 is of degree 3 + 2 = 5.
What is 5x cube -45x?
y = 5x^3 - 45x is a polynomial equation that crosses the y axis at x=3.
At most how many unique roots will a third-degree polynomial have?
A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021
What is a zero of polynomial function?
A zero of a polynomial function - or of any function, for that matter - is a value of the independent variable (often called "x") for which the function evaluates to zero. In other words, a solution to the equation P(x) = 0. For example, if your polynomial is x2 - x, the corresponding equation is x2 - x = 0. Solutions to this equation - and thus, zeros to the polynomial - are x = 0, and x = 1.
If 3 - 2i is a solution to a polynomial equation is the complex conjugate 3 plus 2i also a solution yes or no?
Not necessarily, take for example the equation x^2=5-12i. Then, 3-2i satisfies the equation. However, 3+2i does not because (3+2i)^2 = 5+12i.
A quadratic polynomial is a third-degree polynomial?
No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).
Why has only two distinct roots in quadratic equation?
This is related to the Fundamental Theorem of Algebra; read about it for more information. Basically, this theorem states that any complex polynomial has at least one root; as a corrolary - in the complex number system - a polynomial of degree "n" can be divided into "n" linear factors. For example, x2 - 5x - 6 can be expressed as (x - 2) (x - 3). (The numbers may be complex for some polynomials.) Therefore, the corresponding equation, x2 - 5x - 6 = 0, can be written as (x - 2) (x - 3) = 0. Since a product can only be zero if at least one of its factors is zero, this lets us split the equation into two parts: (x - 2) (x - 3) = 0 is equivalent to (x - 2) = 0 or (x - 3) = 0. Each linear equation has one solution; the equation thus has two solutions. (However, there may be repeated solutions, depending on the polynomial.)
