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`

Expert Answers
tiburtius eNotes educator| Certified Educator

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.

oldnick | Student

`-14x^4-28x^3=0`   (multiplied by 10)

`14x^3(x+2)=0`        (Changed sign)

`14x=0 `   `x=0`   (its a three value root)

`x+2=0`    `x=-2`

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`