Find the zeros of the polynomial function and state the multiplicity of each.
F(x) =(x^2 -5x+6)^2
isnt this the same as ..
f(x)=((x-3)(x-2))^2 ?
3, and 2 are double roots.
Yes but I need to find the zeros of the polynomial function and state the multiplicity of each.
As bobpursley said, the zeroes or roots are 3 and 2 from factoring the function into ((x-3)(x-2))^2.
Both are double roots, or to the power of 2, because both are squared.
To find the zeros of the polynomial function, we need to set F(x) equal to zero and solve for x.
F(x) = (x^2 - 5x + 6)^2 = 0
Now, since we have a squared term, we know that the function will have two identical factors that equal zero. So we need to find the roots of the quadratic equation (x^2 - 5x + 6) = 0 and determine their multiplicity.
To solve the quadratic equation, we can factorize it:
(x^2 - 5x + 6) = (x - 2)(x - 3)
Now we can set each factor equal to zero:
x - 2 = 0 or x - 3 = 0
Solving these equations will give us the values of x:
x = 2 or x = 3
So the zeros of the polynomial function F(x) are x = 2 and x = 3.
To determine the multiplicity of each zero, we look at the exponent of the corresponding factor in the factored form of the polynomial. In this case, the factor (x - 2) appears twice, and the factor (x - 3) also appears twice. This means that each zero has a multiplicity of 2.
Hence, the zeros of the polynomial function F(x) = (x^2 - 5x + 6)^2 are x = 2 and x = 3, both with a multiplicity of 2.