Question

polynomial equation whose roots are alpha,beta,gamma ​

Answer 1

Answer:

ax³+ bx² + cx + d = 0

cubic polynomial.

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Answer 2

Given: Roots of the equation are $\alpha,\ \beta,\ \gamma$.

The roots can be written as,

$(x-\alpha)=0, \ (x-\beta)=0, \ (x-\gamma)=0$

So we can write as,

$(x-\alpha)\ (x-\beta) \ (x-\gamma)=0\\(x^2-\alpha x-\beta x+\alpha\beta)(x-\gamma)=0\\x^3-\alpha x^2-\beta x^2+\alpha\beta x -\gamma x^2-\alpha \gamma x-\beta \gamma x-\alpha\beta\gamma=0\\x^3- x^2(\alpha +\beta +\gamma )+x(\alpha\beta -\alpha \gamma -\beta \gamma)-\alpha\beta\gamma=0$

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