Question

if alpha beta gamma are the zeros of the polynomial p x such that alpha + beta + Gamma is equals to 3 alpha beta + beta Gamma + Gamma Alpha is equals to minus 10 and alpha beta gamma is equals to minus -24, P(x) is ​

Answer 1

$\textbf{Given:}$

$\text{ \alpha,\beta and \gamma are zeros of P(x) }$

$\alpha+\beta+\gamma=3$

$\alpha\beta+\beta\gamma+\gamma\alpha=-10$

$\alpha\beta\gamma=-24$

$\textbf{To find:}$

$P(x)$

$\textbf{Solution:}$

$\text{We know that,}$

$\textbf{The cubic polynomial having zeros \bf\,\alpha,\beta and \bf\,\gamma is}$

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

$\text{The required polynomial is}$

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

$=x^3-(3)x^2+(-10)x-(-24)$

$=x^3-3x^2-10x+24$

$\textbf{Answer:}$

$\textbf{Option (C) is correct}$

Find more:

Form a cubic polynomial whose zeroes are 2 , 1 , 1.

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Answer 2

Answer:

x^3-3x^2-10x+24

Step-by-step explanation:

FIND YOURSELF

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