Question

A cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeros are 2, -7, and -14 respectively, is (a) x^3-2x^2 - 7x +14 (b) x^3 + 2x^2 +7x+14 (c) x^3 - 2x^2 -7x-14 (d) x^3 +2x^2-7x-14 solve the question

Answer 1

• Option (D) is correct answer.

☛☛Refer to the attachment for detailed solution. {Sorry for bad handwriting}

↪ Something To Be Known :

• Cubic Polynomial's highest degree is 3.

• Thus, They have atmost three zeroes.

• General Form of Cubic Polynomial is $\rm {ax}^{3} + {bx}^{2} + cx + d$, where a, b, c, and d are real numbers & $\rm a\neq0$.

• Standard form of cubic polynomial is $\small \rm x^{3}+({\alpha}+{\beta}+{\gamma})x^{2}+({\alpha}{\beta}+{\beta}{\gamma}+{\alpha}{\gamma}) x+ {\alpha}{\beta}{\gamma}$, where ${\alpha}, \:{\beta}, and \:{\gamma}$ are zeroes of the polynomial.