Question

find a cubic polynomial whose zeros are 3 , 1/2and -1

Answer 1

Answer:

$\red { Required \:cubic \: polynomial :}$

$\green { = 2x^{3} - 5x^{2} - 4x + 3 }$

Step-by-step explanation:

$Let \:\alpha ,\beta \:and \:\gamma \:are \:$

$zeroes \: of \: a \:cubic \: polynomial$

$\alpha = 3, \beta = \frac{1}{2}\:and \: \gamma = -1\:(given)$

$\pink { Required \: cubic \: polynomial}$

$\pink { k(x-\alpha)(x-\beta)(x-\gamma)}$

$= k( x -3)\left(x-\frac{1}{2}\right)(x+1)$

$= k(x-3)(x+1)\left(x-\frac{1}{2}\right)$

$= k(x^{2} -2x -3)\left(x-\frac{1}{2}\right)$

$= k\left( x^{3} -\frac{x^{2}}{2}-2x^{2}+x-3x+\frac{3}{2}\right)$

/* We can put different values of k .

When k = 2 , the Quadratic polynomial will be

$= 2x^{3} - x^{2} -4x^{2} + 2x - 6x +3$

$= 2x^{3} - 5x^{2} - 4x + 3$

Therefore.,

$\red { Required \:cubic \: polynomial :}$

$\green { = 2x^{3} - 5x^{2} - 4x + 3 }$

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Answer 2

Step-by-step explanation:

a+b+y=3

ab+ by+ ya=1/2

aby=-1

k(x³-a +b+ y)x²+ab-by+ya)x-aby