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Answers
Given : polynomial 2x⁴ + 6x³ - x² - 15x - 10 and two zeroes √(5/2) & - √(5/2)
To find : other zeroes
Solution:
Two of the zeroes are √(5/2) & - √(5/2)
=> (x - √(5/2) ) (x - (-√(5/2) ) is factor of polynomial
=> (x - √(5/2) ) (x + √(5/2) ) is factor of polynomial
=> ( x² - 5/2) is factor of polynomial
=> (2x² - 5) is factor of polynomial
x² + 3x + 2
2x² - 5 _| 2x⁴ + 6x³ - x² - 15x - 10 |_
2x⁴ -5x²
_______________
6x³ + 4x² - 15x - 10
6x³ -15x
________________
4x² -10
4x² -10
___________
0
____________
2x⁴ + 6x³ - x² - 15x - 10 = (2x² - 5) ( x² + 3x + 2)
x² + 3x + 2 = 0
=> x² + 2x + x + 2 = 0
=> x(x + 2) + 1 (x + 2) = 0
=> (x + 1)(x + 2) = 0
=> x = - 1 & - 2
other zeroes are - 1 & - 2
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