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What are the zeros of the polynomial function f(x) = x3 - 10x2 + 24x? I just want to know the name of the process to find the zeros.

2 Answers

3 votes

f(x) = x³- 10x² + 24x

f(x) = x ( x² + 10x + 24)

f(x) = x (x + 6)(x+4)

x=0


-----------------
x+6 = 0
x = 0-6
x= -6


-------------
x+4 = 0
x = 0-4
x= -4

zero's would be: 0, -6 and -4,
So it is your third choice down.
User Agilefall
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5 votes

Answer:

A zero of a function is a number, when plugged in for the variable, makes the function equal to zero.

Then, the roots of a polynomial P(x) are values of x such that P(x) = 0.

Given the polynomial function:
f(x)=x^3-10x^2+24x

By the rational theorem process, gives us the following possible roots: 0,
\pm 1,
\pm 2,
\pm 3 ,
\pm 4,
\pm 6,
\pm 8,
\pm 12 and
\pm 24

for x =0


f(0)=0^3-10(0)^2+24(0)=0

Now, our polynomial become:


x(x^2-10x+24) = 0

Then, we factors the remaining quadratic equation, factoring by grouping , using the facts 4+6 = 10 and
4 \cdot 6 = 24


x(x^2-6x-4x+24) = 0


x(x(x-6)-4(x-6)) =0


x((x-6)(x-4)) =0

Zero product property states that if xy = 0 then either a =0 or b =0.

by zero product property;

⇒ x = 0, x-6=0 and x-4 = 0

Hence, x = 0 , x = 4 and x =6 are the zeros of the given polynomial function.

User Valery Miller
by
8.0k points

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