Answer:
The solutions of the equation are 0 and 0.75.
Step-by-step explanation:
Given : Equation [tex]16x^4 - 24x^3 +9x^2 =0[/tex]
To find : All solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically ?
Solution :
Equation [tex]16x^4 - 24x^3 +9x^2 =0[/tex]
[tex]x^2(16x^2-24x+9)=0[/tex]
Either [tex]x^2=0[/tex] or [tex]16x^2-24x+9=0[/tex]
When [tex]x^2=0[/tex]
[tex]x=0[/tex]
When [tex]16x^2-24x+9=0[/tex]
Solve by quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-24)\pm\sqrt{(-24)^2-4(16)(9)}}{2(16)}[/tex]
[tex]x=\frac{24\pm\sqrt{0}}{32}[/tex]
[tex]x=\frac{24}{32}[/tex]
[tex]x=\frac{3}{4}[/tex]
[tex]x=0.75[/tex]
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.