Question

α, β and ​γ ​are the zeroes of the cubic polynomial p(x) = ax3 + bx2 + cx + d. If the values of α+β+γ, αβ+βγ+αγ and αβγ are (-1/2), (-5/2) and (-1) respectively, then the polynomial p(x) is?​
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Answer 1

Dear Student,

$$\begin{gathered} \mathrm{The}\mathrm{equation}\mathrm{will}\mathrm{be} \\ {\mathrm{x}}^3-\left(\mathrm{sum}\mathrm{of}\mathrm{roots}\right){\mathrm{x}}^2+\left(\mathrm{product}\mathrm{of}\mathrm{roots}\mathrm{taken}\mathrm{two}\mathrm{at}\mathrm{a}\mathrm{time}\right)\mathrm{x}-\mathrm{product}\mathrm{of}\mathrm{roots} \\ ={\mathrm{x}}^3-\left(\frac{-1}{2}\right){\mathrm{x}}^2-\frac{5\mathrm{x}}{2}-\left(-1\right) \\ \mathrm{or} \\ 2{\mathrm{x}}^3+{\mathrm{x}}^2-5\mathrm{x}+2=0 \end{gathered}$$
Regards