Kind a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.
Let the quadratic polynomial be ax3 +bx2 +cx + d and its zeroes be α, β and ϒ.
We have,
![straight alpha plus straight beta plus straight gamma space equals space 2 over 1 equals negative fraction numerator Coefficient space of space straight x squared over denominator Coefficient space of space straight x cubed end fraction equals negative straight b over straight a](/application/zrc/images/qvar/MAEN10041308.png)
![αβ plus βγ plus γα equals fraction numerator negative 7 over denominator 1 end fraction equals fraction numerator Coefficient space of space straight x over denominator Coefficient space of space straight x cubed end fraction equals straight c over straight a](/application/zrc/images/qvar/MAEN10041308-1.png)
and ![space space space space αβγ equals fraction numerator negative 14 over denominator 1 end fraction equals negative fraction numerator Constant space term over denominator Coefficient space of space straight x cubed end fraction equals fraction numerator negative straight d over denominator straight a end fraction](/application/zrc/images/qvar/MAEN10041308-2.png)
When we put a = 1, then b = -2, c=-7, d = 14.
Therefore, the required cubic polynomial be x3 – 2x2 – 7x + 14.
270 Views