find the real zeros of the polynomial function and state their multiplicities. explain how you arrived at your answer. `f(x)=-1.4x^4-2.8x^3`
You need to find roots of `-1.4x^4-2.8x^3=0`
Let's rewrite this as
Now we have product and product will be equal to 0 if at least one of the terms is equal to 0 and thus we get two equations
This root has multiplicity of 3 because that is equation of third degree which has 3 roots and each of them is 0.
And this root has multiplicity of 1 because we got it by solving linear equation which has only one root.
Since we had equation of fourth degree and we got one root with multiplicity 3 and one with multiplicity 1 which means we have all of the solutions to the equation.
`-14x^4-28x^3=0` (multiplied by 10)
`14x^3(x+2)=0` (Changed sign)
`14x=0 ` `x=0` (its a three value root)
So equation has roots:
`x_1=0` `x_2=0` `x_3=0` `x_4=-2`
It's looks like function hasonly two root, for doesn not report the multiciply of root `x=0`