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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.
Can a polynomial be no rational zeros but have real zeros?
Yes, a polynomial can have no rational zeros while still having real zeros. This occurs, for example, in the case of a polynomial like (x^2 - 2), which has real zeros ((\sqrt{2}) and (-\sqrt{2})) but no rational zeros. According to the Rational Root Theorem, any rational root must be a factor of the constant term, and if none exist among the possible candidates, the polynomial can still have irrational real roots.
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 are the zeros of polynomials?
The values of the variables which make the polynomial equal to zero
What are the zeros of polynomial x2-16?
The zeros of the polynomial ( x^2 - 16 ) can be found by setting the equation equal to zero: ( x^2 - 16 = 0 ). This can be factored as ( (x - 4)(x + 4) = 0 ). Therefore, the zeros are ( x = 4 ) and ( x = -4 ).
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.
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.
-2,1,4?
Polynomial fuction in standard form with the given zeros
Sum and product of the zeros of a quadratic polynomial are -12 and -3 respectively what is the quadratic polynomial?
x2 + 15x +36
What are the zeros of polynomials?
The values of the variables which make the polynomial equal to zero
How do you find polynomial whose zeros are given?
when the equation is equal to zero. . .:)
Is the x-intercepts the same thing as zeros?
Yes, the places where the graph of a polynomial intercepts the x-axis are zeros. The value of y at those places must be 0 for the polynomial to intersect the x axis.
What is the factor theorem?
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
What does factor theorem mean?
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
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
How do you graph a polynomial in order to solve for the Zeros?
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
