Find the cubic polynomial whose zeros are 5, - 2,1/3
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Cubic polynomial is a polynomial of degree 3 , It's general form is ax³+bx²+cx+d , It can have atmost 3 zeroes.
Given zeroes of cubic polynomial = 5 , -2 , 1/3 .
So, x - 5 , x + 2 , x - 1/3 are factors of the polynomial .
Cubic polynomial
= ( x - 5 ) ( x + 2 ) ( x - 1/3)
= (x² -5x + 2x - 10 )( x - 1/3 )
= ( x² - 3x - 10 )( x - 1/3 )
= x ( x² - 3x - 10 ) - 1/3 ( x² - 3x - 10 )
= x³ -3x² - 10x - x²/3 + x + 10/3
Multiplying by 3
= 3x³ -9x² - 30x - x² - 3x + 10
= 3x³ - 10x² - 33x + 10
Therefore, The required cubic polynomial is ( 3x³ - 10x² - 33x + 10 )
Cubic polynomial is a polynomial of degree 3 , It's general form is ax³+bx²+cx+d , It can have atmost 3 zeroes.
Given zeroes of cubic polynomial = 5 , -2 , 1/3 .
So, x - 5 , x + 2 , x - 1/3 are factors of the polynomial .
Cubic polynomial
= ( x - 5 ) ( x + 2 ) ( x - 1/3)
= (x² -5x + 2x - 10 )( x - 1/3 )
= ( x² - 3x - 10 )( x - 1/3 )
= x ( x² - 3x - 10 ) - 1/3 ( x² - 3x - 10 )
= x³ -3x² - 10x - x²/3 + x + 10/3
Multiplying by 3
= 3x³ -9x² - 30x - x² - 3x + 10
= 3x³ - 10x² - 33x + 10
Therefore, The required cubic polynomial is ( 3x³ - 10x² - 33x + 10 )
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