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8.3
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Answer ⇒ a = -2/3
Step-by-step explanation ⇒ As per as the given question, x + 2a divides the polynomial x⁵ - 4a²x³ + 2x + 2a + 3 completely.
This means, if we put x = -2a in the given polynomial then we will get the value of polynomial as zero. That's whats the factor theorem says.
∴ (-2a)⁵ - 4a²(-2a)³ + 2a + 3 = 0
∴ -32a⁵ + 32a⁵ + 2a + 3 = 0
∴ 0 = 2a + 3
∴ a = -2/3
Hence, the value of a is -2/3.
Hope it helps.
Answered by
1
Answer:As per as the given question, x + 2a divides the polynomial x⁵ - 4a²x³ + 2x + 2a + 3 completely.
This means, if we put x = -2a in the given polynomial then we will get the value of polynomial as zero. That's whats the factor theorem says.
∴ (-2a)⁵ - 4a²(-2a)³ + 2a + 3 = 0
∴ -32a⁵ + 32a⁵ + 2a + 3 = 0
∴ 0 = 2a + 3
∴ a = -2/3
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