Question

Find all solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically. (Enter your answers as a comma-separated list.) 16x^4 - 24x^3 +9x^2 =0

Answer 1

The solutions of the equation are 0 and 0.75.

Explanation:

Given : Equation
`16x^4 - 24x^3 +9x^2 =0`

To find : All solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically ?

Solution :

Equation
`16x^4 - 24x^3 +9x^2 =0`

`x^2(16x^2-24x+9)=0`

Either
`x^2=0` or
`16x^2-24x+9=0`

When
`x^2=0`

`x=0`

When
`16x^2-24x+9=0`

Solve by quadratic formula,
`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-24)\pm√((-24)^2-4(16)(9)))/(2(16))`

`x=(24\pm√(0))/(32)`

`x=(24)/(32)`

`x=(3)/(4)`

`x=0.75`

The solutions of the equation are 0 and 0.75.

For verification,

In the graph where the curve cut x-axis is the solution of the equation.

Refer the attached figure below.