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Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, –2 and –24 respectively.
The required cubic polynomial can be calculated as:
x3 – (Sum of the zeros) x2 + (Sum of the product of the zeros taking two at a time) x – Product of Zeros
It is given that, product of the zeros are 5, -2 and – 24 respectively
Putting these values in the equation, we get:
x3 – 5x2 – 2x + 24