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.
by synthetic division and quadratic equation
Try the quadratic formula. X = -b ± (sqrt(b^2-4ac)/2a)
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
Polynomial fuction in standard form with the given zeros
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.
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.
The values of the variables which make the polynomial equal to zero
when the equation is equal to zero. . .:)
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.
There are 3 zeros in the product.