find the zeros of 5x(x2-4x-1)
the only example the book gives is -2x4+2x2 and the teacher hasn't gone over this in detail in class. I'm lost talk me thru it please.
The "zeroes" of f(x) are those values of x for which f(x) = 0. Another word for the same thing is "roots." Are you clear on the definition?
A polynomial of degree n is defined as
Pn(x)=i=1∑n+1aixn+1−i,a1=0.
That is, a polynomial in x of degree n is a sum, where each summand is a number times a power of x, and the highest power is n. Very simple.
Do you understand what a polynomial is?
A polynomial of degree n has AT MOST n distinct real zeroes.
A polynomial with real zeroes can be factored into linear terms, where each linear term is x MINUS the real root.
Finding the zeroes of a polynomial is frequently a matter of factoring it. (There are general ways to solve quadratics, cubics, and quartics that do not require factoring.)
So let's look at the book's example.
Where does −2x4+2x2=0?
Let's factor
−2x4+2x2=2(x2)(x2−1)=0.
But we want differences with x.
2(x2)(x2−1)=2(x−0)2(x−1)(x+1)=0.
That means the zeroes are: 0, 1, and−1.
Lets check
−2(0)4+2(0)2=−2∗0+2∗0=0+0=0. OK.
−2(1)4+2(1)2=−2∗1+2∗1=−2+2=0. OK.
−2(−1)4+2(−1)2=−2∗1+2∗1=−2+2=0. OK.
OK The problem you gave is ALREADY partially factored. Complete factoring. Can you figure out the zeroes now?
