find a polynomial f(x) of degree 4 that has the following zeros:
0,7,-4,5
Leave your answer in factored form
To find the polynomial with the given zeros, we can use the zero-product property. Since the zeros are 0, 7, -4, and 5, the factored form of the polynomial can be expressed as:
f(x) = (x - 0)(x - 7)(x + 4)(x - 5)
Expanding this expression, we get:
f(x) = (x)(x - 7)(x + 4)(x - 5)
Therefore, the polynomial f(x) of degree 4 with the given zeros is:
f(x) = x^4 - 8x^3 + 33x^2 - 140x
To find a polynomial in factored form with the given zeros, we can use the zero-product property. The zero-product property states that if a product of factors is equal to zero, then at least one of the factors must be zero.
If the zeros of the polynomial are 0, 7, -4, and 5, then we can write the factored form as:
f(x) = (x - 0)(x - 7)(x - (-4))(x - 5)
Simplifying this expression yields:
f(x) = x(x - 7)(x + 4)(x - 5)
So, the polynomial f(x) in factored form that has the given zeros is:
f(x) = x(x - 7)(x + 4)(x - 5)
find a polynomial f(x) of degree 4 that has the following zeros:
-1,7,0,-4
Leave your answer in factored form
(x-0)(x-7)(x+4)(x-5) = 0
(x^2 -7x)(x^2-x -20) = 0
x^2(x^2-x-20)-7x(x^2-x -20)
= x^4 -x^3 - 20 x^2 - 7x^3 + 7x^2 + 140 x
= x^4 - 8 x^3 - 13 x^2 + 140 x