find a cubic polynomial whose zeroes are 3,half and _1
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let a, b and c be zero so there are 3 zeroes and 1/2 is -1
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Let the zeros be a , b , c which are 3 , 1/2 , -1 respectively .
For a cubic polynomial
Sum of zeros = a + b + c
= 3 + 1/2 -1
= 2.5
Sum of product of two zeros = ab + bc + ac
= 3 × 1/2 + 1/2 × (-1) + 3 × (-1)
= 1.5 - 1.5 - 3
= -3
Product of all zeros = abc
= 3 × 1/2 × (-1)
= -1.5
Therefore the required cubic polynomial is = x³ + ( a + b + c ) x² - ( ab + bc + ac ) x
+ ( abc )
= x³ + 2.5x² + 3x -1.5
For a cubic polynomial
Sum of zeros = a + b + c
= 3 + 1/2 -1
= 2.5
Sum of product of two zeros = ab + bc + ac
= 3 × 1/2 + 1/2 × (-1) + 3 × (-1)
= 1.5 - 1.5 - 3
= -3
Product of all zeros = abc
= 3 × 1/2 × (-1)
= -1.5
Therefore the required cubic polynomial is = x³ + ( a + b + c ) x² - ( ab + bc + ac ) x
+ ( abc )
= x³ + 2.5x² + 3x -1.5
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