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Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2?
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Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x +...
Given Problem:
To find the value of 'a' if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2.
Solution:
Step 1: Write the given polynomial equation
Let the given polynomial equation be P(x) = x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2.
Step 2: Apply the factor theorem
If x + 2a is a factor of P(x), then P(-2a) should be equal to 0.
P(-2a) = (-2a)^4 + 2a(-2a)^3 + 5(-2a)^2 + 9(-2a) + 18 - 20a^2
Simplify the above expression and set it equal to 0 to find the value of 'a'.
Step 3: Solve for 'a'
(-2a)^4 + 2a(-2a)^3 + 5(-2a)^2 + 9(-2a) + 18 - 20a^2 = 0
16a^4 - 16a^4 + 20a^2 - 18a + 18 - 20a^2 = 0
-18a + 18 = 0
a = 1
Therefore, the value of 'a' is 1 if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2.
To find the value of 'a' if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2.
Solution:
Step 1: Write the given polynomial equation
Let the given polynomial equation be P(x) = x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2.
Step 2: Apply the factor theorem
If x + 2a is a factor of P(x), then P(-2a) should be equal to 0.
P(-2a) = (-2a)^4 + 2a(-2a)^3 + 5(-2a)^2 + 9(-2a) + 18 - 20a^2
Simplify the above expression and set it equal to 0 to find the value of 'a'.
Step 3: Solve for 'a'
(-2a)^4 + 2a(-2a)^3 + 5(-2a)^2 + 9(-2a) + 18 - 20a^2 = 0
16a^4 - 16a^4 + 20a^2 - 18a + 18 - 20a^2 = 0
-18a + 18 = 0
a = 1
Therefore, the value of 'a' is 1 if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2.
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Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2?
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Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2?.
Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a if x + 2a is a factor of x^4 + 2ax^3 + 5x^2 + 9x + 18 - 20a^2?.
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