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How do you find the zeros of any given polynomial function?
by synthetic division and quadratic equation
How can you use a graph to find zeros of a quadratic function?
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
What happens if there are no zeros in a quadratic function?
Whether or not a function has zeros depends on the domain over which it is defined.For example, the linear equation 2x = 3 has no zeros if the domain is the set of integers (whole numbers) but if you allow rational numbers then x = 1.5 is a zero.A quadratic function such as x^2 = 2 has no rational zeros, but it does have irrational zeros which are sqrt(2) and -sqrt(2).Similarly, a quadratic equation need not have real zeros. It will have zeros if the domain is extended to the complex field.In the coordinate plane, a quadratic without zeros will either be wholly above the horizontal axis or wholly below it.
How do you use quadratic formula on ti 89?
The function on a ti-89 that gives you the zeros of a quadratic equation is called just that "zeros". To access it from the home screen, press f2 and select the label called "zeros(" then type the function and define the variable. For example: if you want the zeros of y=x^2+7x+12 you the display should read: zeros(x^2+7x+12,x), press enter and it will give you the results in this case {-3, -4}. We can check if it did it right by factoring this simple quadratic. 0=x^2+7x+12 factors as 0=(x+3)(x+4) set the factors equal to zero: x+3=0 x=-3 x+4=0 x=-4 So we see that the calculator did it right! That is always a good thing. This will work for most polynomial functions.
What are the factors of a polynomial function with zeros at -2 and 7?
Since there are two zeros, we have: y = (x - (-2))(x - 7) y = (x + 2)(x - 7)
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.
How do you find the zeros of any given polynomial function?
by synthetic division and quadratic equation
Formula for finding zeros of polynomial function?
Try the quadratic formula. X = -b ± (sqrt(b^2-4ac)/2a)
How you Find the quadratic polynomial whose zeros are 2 and -3?
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 ).
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 relationship between zeros and factors?
Zeros and factors are closely related in polynomial functions. A zero of a polynomial is a value of the variable that makes the polynomial equal to zero, while a factor is a polynomial that divides another polynomial without leaving a remainder. If ( x = r ) is a zero of a polynomial ( P(x) ), then ( (x - r) ) is a factor of ( P(x) ). Thus, finding the zeros of a polynomial is equivalent to identifying its factors.
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 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.
How can you use a graph to find zeros of a quadratic function?
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
State whether the following is a polynomial function give the zero s of the function if the exist f x x 2-6x plus 8?
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.
7w squared minus 17w plus 16?
7w2 -17w+16 is a polynomial that cannot be factored. We call this a prime polynomial.There are also no like terms to combine. So nothing much more can be done with this polynomial. If you wanted to find the roots or the zeros, you could use the quadratic formula.
How many zeros can be a polynomial of degree 'n' have?
A polynomial of degree ( n ) can have at most ( n ) distinct zeros (roots) in the complex number system, according to the Fundamental Theorem of Algebra. These zeros may be real or complex, and they can also be repeated, meaning a polynomial can have fewer than ( n ) distinct zeros if some are counted multiple times (multiplicity). For example, a polynomial of degree 3 could have 3 distinct zeros, 2 distinct zeros (one with multiplicity 2), or 1 distinct zero (with multiplicity 3).
