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What is the LARGEST number of real zeros a polynomial with degree n can have?
A polynomial of degree ( n ) can have at most ( n ) real zeros. This is a consequence of the Fundamental Theorem of Algebra, which states that a polynomial of degree ( n ) has exactly ( n ) roots in the complex number system, counting multiplicities. Therefore, while all roots can be real, the maximum number of distinct real zeros a polynomial can possess is ( n ).
What is a polynomial function f of least degree that has rational coefficient a leading coefficient of 1 and the given zeros -7 -4?
A polynomial function of least degree with rational coefficients and a leading coefficient of 1 that has the zeros -7 and -4 can be constructed using the fact that if ( r ) is a zero, then ( (x - r) ) is a factor. Therefore, the polynomial can be expressed as ( f(x) = (x + 7)(x + 4) ). Expanding this, we get ( f(x) = x^2 + 11x + 28 ). Thus, the polynomial function is ( f(x) = x^2 + 11x + 28 ).
What do you know about the most possible number of zeros for a polynomial?
A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.
Is it possible that the polynomial function doesn't have zeros?
In the real domain, yes. In the complex domain, no.
What is a quadratic polynomial which has no zeros?
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
If you are asked to write a polynomial function of least degree with real coefficients and with zeros of 2 and i square roots of seven what would be the degree of the polynomial also wright equation?
3y2-5xyz yay i figured it out!!!!
What do the zeros of a polynomial function represent on a graph?
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
What is the LARGEST number of real zeros a polynomial with degree n can have?
A polynomial of degree ( n ) can have at most ( n ) real zeros. This is a consequence of the Fundamental Theorem of Algebra, which states that a polynomial of degree ( n ) has exactly ( n ) roots in the complex number system, counting multiplicities. Therefore, while all roots can be real, the maximum number of distinct real zeros a polynomial can possess is ( n ).
What is a polynomial function f of least degree that has rational coefficient a leading coefficient of 1 and the given zeros -7 -4?
A polynomial function of least degree with rational coefficients and a leading coefficient of 1 that has the zeros -7 and -4 can be constructed using the fact that if ( r ) is a zero, then ( (x - r) ) is a factor. Therefore, the polynomial can be expressed as ( f(x) = (x + 7)(x + 4) ). Expanding this, we get ( f(x) = x^2 + 11x + 28 ). Thus, the polynomial function is ( f(x) = x^2 + 11x + 28 ).
What do you know about the most possible number of zeros for a polynomial?
A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.
What are the zeros of a polynomial function?
the zeros of a function is/are the values of the variables in the function that makes/make the function zero. for example: In f(x) = x2 -7x + 10, the zeros of the function are 2 and 5 because these will make the function zero.
Is it possible that the polynomial function doesn't have zeros?
In the real domain, yes. In the complex domain, no.
How do you find the zeros of any given polynomial function?
by synthetic division and quadratic equation
what are all of the zeros of this polynomial function f(a)=a^4-81?
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 ...
What is a quadratic polynomial which has no zeros?
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
Is it possible for a polynomial function of degree 3 to have no real zeros?
Yes - but only if the domain is restricted. Normally the domain is the whole of the real numbers and over that domain it must have at least one real zero.
What is the remainder thereom?
The remainder theorem states that if you divide a polynomial function by one of it's linier factors it's degree will be decreased by one. This theorem is often used to find the imaginary zeros of polynomial functions by reducing them to quadratics at which point they can be solved by using the quadratic formula.
