The question is find the zeros of the function the problem is f(x)= 9x^4-25x^2

Makena Preston

Makena Preston

Answered question

2022-07-26

The question is find the zeros of the function
the problem is f ( x ) = 9 x 4 25 x 2

Answer & Explanation

agyalapi60

agyalapi60

Beginner2022-07-27Added 17 answers

zeros function:
9 x 4 25 x 2 = x 2 ( 9 x 2 25 ) note that 9 x 2 25 < apply different square( or perfectsquare)
= x 2 ( 3 x 5 ) ( 3 x + 5 )
now set x 2 = 0 x = 0 solution 1
3x-5=0 solve for x: x = 5 3
3x+5=0 solve for x: x = 5 3
solutions are: x = 5 3 , 0 , 5 3
prkosnognm

prkosnognm

Beginner2022-07-28Added 5 answers

Find the zeros of the function
the problem is f ( x ) = 9 x 4 25 x 2
First of all, this is a polynomial function of 4thdegree. It is called a 4th degree polynomial because thehighest exponent is has is 4.
Secondly, f(x) = y and vice-versa, which means the two termsare interchangeable.
Let f(x) or y = 0....USE EITHER ONE and replace by zero.
0 = 9 x 4 25 x 2
We factor the right side of the equation. Factor out x 2
x 2 ( 9 x 2 25 x 2 )
Divide 9 x 4 and 25 x 2 by x 2
Doing so, we get this:
0 = x 2 ( 9 x 2 25 )
We now have to factor what lies inside the parentheses.
9 x 2 25 = ( 3 x 5 ) ( 3 x + 5 )
We now have THREE factors and they are:
x 2 , (3x-5) and (3x+5)
We set each factor to 0 and solve for x.
I assume that you know how to solve for x for quadratic andlinear functions, right?
For the x square term, we take the square root of both sidesto find our x.
x 2 = 0 becomes x=0 This is our first zero.
3x - 5 = 0
3x = 5
x = 5/3...This is our second zero.
NEXT:
3x + 5 = 0
3x = -5
x = -5/3...This is our third zero.
Here are the threezeroes of the original polynomial function:
x = 0, x = 5/3 and x = -5/3

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