A polynomial whos zeroes are 1/alpha^2and1/beta^2
Answers
Step-by-step explanation:
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Answer:Step-by-step explanation:
Quadratic polynomial : 6x² - 7x + 2
α, β are the zeroes of the polynomial
Comparing 6x² - 7x + 2 with ax² + bx + c we get,
a = 6
b = - 7
c = 2
Sum of zeroes = α + β = - b / a = - ( - 7 ) / 6 = 7 / 6
Product of zeroes = αβ = c / a = 2 / 6
If 1 / α , 1 / β are zeroes of the polynomial
Sum of zeroes = 1 / α + 1 / β = ( α + β ) / αβ = ( 7 / 6 ) / ( 2 / 6 ) = 7 / 2
Product of zeroes = ( 1 / α ) × ( 1 / β ) = 1 / αβ = 1 / ( 2 / 6 ) = 6 / 2
Quadractic polynomial :
= k{ x² - ( Sum )x + Product }
[ Where k ≠ 0 ]
= k{ x² - ( 7/2 )x + 6/2 }
= k( x² - 7x/2 + 6/2 )
When k = 2
= 2( x² - 7x/2 + 6/2 )
= 2x² - 7x + 6
Hence the required quadratic polynomial is 2x² - 7x + 6.