Find the quadratic polynomial whose zeros are 1/2 & -1/2
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Answer:
The quadratic polynomial is 4x² - 1.
Step-by-step explanation:
Sum of the quadratic polynomial = 1/2 - 1/2 = 0
Product of the quadratic polynomial = 1/2 ( - 1/2 ) = - 1/4
Quadratic polynomial = k{ x² - (Sum)x + Product }
Where k ≠ 0
= k( x² - 0x - 1/4 )
= k( x² - 1/4 )
When k = 4
= 4( x² - 1/4 )
= 4x² - 1
Therefore the quadratic polynomial is 4x² - 1.
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