Find all solutions of the equation algebraically.

Ответ:

jwhit28

02.01.2022

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.

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