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What else can I help you with?
What is the correct classification of x2 plus 3x plus 8?
It is a quadratic polynomial with integer coefficients..
What two kinds of coefficients of friction exist?
Static and kinetic coefficients
Can a constant be considered a polynomial?
No, a constant cannot be considered a polynomial because it is only a single term. A polynomial is defined as an expression that consists of the variables and coefficients that involves only the operations of subtraction, addition, multiplication, and the non-negative integer exponents.
What is algebraic numbers?
An algebraic number is one that is a root to a non-zero polynomial, in one variable, whose coefficients are rational numbers.Equivalently, if the polynomial is multiplied by the LCM of the coefficients, the coefficients of the polynomial will all be integers.
How do I find the discriminant?
Given the quadratic equation ax^2 + bx + c =0, where a, b, and c are real numbers: (The discriminant is equal to b^2 - 4ac) If b^2 - 4ac < 0, there are two conjugate imaginary roots. If b^2 - 4ac = 0, there is one real root (called double root) If b^2 - 4ac > 0, there are two different real roots. In the special case when the equation has integral coefficients (means that all coefficients are integers), and b^2 - 4ac is the square of an integer, the equation has rational roots. That is , if b^2 - 4ac is the square of an integer, then ax^2 + bx + c has factors with integral coefficients. * * * * * Strictly speaking, the last part of the last sentence is not true. For example, consider the equation 4x2 + 8x + 3 = 0 the discriminant is 16, which is a perfect square and the equation can be written as (2x+1)*(2x+3) = 0 To that extent the above is correct. However, the equation can also be written, in factorised form, as (x+1/2)*(x+3/2) = 0 Not all integral coefficients.
If a polynomial cannot be factored using integer coefficients then it is?
In that case, it may, or may not, be possible to factor it using non-integer coefficients.
What is an algebraic integer?
An algebraic integer is a number which is a root of a monic polynomial whose coefficients are integers.
What is the Integer placed in front of an element's formula called?
coefficients
What rule describes a pattern that will have even numbers?
It can be any polynomial rule with integer coefficients in which there are an even number of odd coefficients.
How does the method for solving equations with fractional or decimal coefficients and constants compare with the method for solving equations with integer coefficients and constants?
The method is the same.
What is the correct classification of x2 plus 3x plus 8?
It is a quadratic polynomial with integer coefficients..
What is type a polynomial with integer coefficients and a leading coefficient of 1 in the box below?
A polynomial with integer coefficients and a leading coefficient of 1 is called a monic polynomial. An example of such a polynomial is ( f(x) = x^3 - 4x^2 + 6x - 2 ). In this polynomial, all coefficients are integers, and the leading term ( x^3 ) has a coefficient of 1.
What is the meaning of rational algebraic expression?
A rational algebraic expression is the ratio of two polynomials, each with rational coefficients. By suitable rescaling, both the polynomials can be made to have integer coefficients.
What are co-efficients?
5x + 3y = 7z 5, 3, and 7 are coefficients and they are integers, they are integer coefficients
Does an equation with an integer coefficient always have an integer solution?
No, an equation with integer coefficients does not always have an integer solution. For example, the equation (2x + 3 = 5) has the integer solution (x = 1), but the equation (x^2 + 1 = 0) has no real solutions, let alone integer ones. The existence of integer solutions depends on the specific form and constraints of the equation.
Can a trinomial x2 plus bx plus c where b and c are integers be factored with integer coefficients if its discriminant is 35?
No.
Will an equation with an integer coefficient always have an integer solution?
No, an equation with integer coefficients does not always have an integer solution. For example, the equation (x + 1 = 2) has an integer solution, (x = 1), but the equation (2x + 3 = 1) has no integer solution since (x = -1) is not an integer. Solutions depend on the specific equation and its constraints, and rational or real solutions may exist instead.
