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

Answer:

The solutions of the equation are 0 and 0.75.

Step-by-step 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, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-24)\pm\sqrt{(-24)^2-4(16)(9)}}{2(16)}$

$x=\frac{24\pm\sqrt{0}}{32}$

$x=\frac{24}{32}$

$x=\frac{3}{4}$

$x=0.75$

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.