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Chapter 12: Q44. (page 637)

Solve each equation.

y4+4y3+4y2=0

Short Answer

Expert verified

The solutions are-2and0.

Step by step solution

01

Step 1. Given Information.

Given, to solve the equation y4+4y3+4y2=0.

02

Step 2. Calculation.

Solving the equation:

y22+2y2鈰�2y+2y2=0y22+y2鈰�2y+y2鈰�2y+2y2=0鈥勨赌勨赌勨赌勨赌勨赌勨赌勨赌�Writingitinthequadraticformy2y2+2y+2yy2+2y=0y2+2yy2+2y=0鈥勨赌勨赌勨赌勨赌勨赌勨赌勨赌勨�勨�勨�勨�勨�勨��Factoringthetrinomialy2+2y2=0y2+2y=0yy+2=0

Using the Zero Product Property:

y=0ory+2=0y=0ory=鈭�2

03

Step 3. Conclusion.

Hence, the solutions are -2 and 0.

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