Mathematics: Consider the function f(x) = x^3 - 15x^2 + 50x.? what are the real zeros in this function?

The number 29 is a prime number, examples of prime numbers are :2,3,5,7 etc...

Consider the function f(x) = x^3 - 15x^2 + 50x.?

bellapimienta8

13.01.2022

We have

f(x)=x^3-15x^2+50x .

To find zeros of this function we equate it with 0

x^3-15x^2+50x=0 .

First we factor out x

x(x^2-15x+50)=0

where we find that first zero is $\boxed{x_1=0}$ .

Then we look at the expression in parentheses

x^2-15x+50=0

using Viéts rule (factorisation)

(x+a)(x+b)=x^2+x(a+b)+ab

we can rewrite the equality

(x-10)(x-5)=0 .

If either of the terms is zero then the equality is true so we get two more zeros $\boxed{x_2=10}$ and $\boxed{x_3=5}$ .

Hope this helps.

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