Question

Find the cubic polynomial with the sum, sum of the product of its zeros taken two at a time and product of its zeros as 3,-1,-3

Answer 1

Answer:

x^3 -3x^2- x + 3

Step-by-step explanation:

Let the polynomial be ax^3+bx^2+cx+d

$\alpha + \beta + \gamma = 3 = - b \div a \\ \alpha \beta + \beta \gamma + \gamma \alpha = - 1 = c \div a \\ \alpha \beta \gamma = - 3 = - d \div a \\ b = - 3 \\ a = 1 \\ c = - 1 \\ d = 3 \\ required \: poynomial = {x}^{3} -3 {x}^{2} - x + 3$

Answer 2

Answer:

Step-by-step explanation:

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