Question

plzz tell this I will mark u as brainlist

Answer 1

$\huge\boxed{\ \ \ \ \ \ \ \ \ \ \huge\boxed{\ \ \ \ \ \ \bold{ x^3-3x^2+4 }\ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ }$

$Because, \\ \\ \\ Let roots of a cubic polynomial be \ \alpha,\ \beta\ and \ \gamma. \\ \\ \\ \therefore\ (x-\alpha)(x-\beta)(x-\gamma) \\ \\ =x^3-(\alpha+\beta+\gamma)x^2+(\alpha\beta+\beta\gamma+\gamma\alpha)x-\alpha\beta\gamma \\ \\ = Let \ x^3+ax^2+bx+c \\ \\ \\ -(\alpha+\beta+\gamma)=a\ \ \ \ \ \Longrightarrow\ \ \ \ \ \alpha+\beta+\gamma=-a \\ \\ \alpha\beta+\beta\gamma+\gamma\alpha=b \\ \\ -\alpha\beta\gamma=c\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Longrightarrow\ \ \ \ \ \alpha\beta\gamma=-c$

$In this question, let the coefficient of \ x^3\ be 1. \\ \\ \\ \alpha+\beta+\gamma=3 \\ \\ -a=3 \\ \\ \therefore\ a=-3 \\ \\ \\ \alpha\beta+\beta\gamma+\gamma\alpha=0 \\ \\ \therefore\ b=0 \\ \\ \\ \alpha\beta\gamma=-4 \\ \\ -c=-4 \\ \\ \therefore\ c=4$

$\therefore\ We can obtain the following cubic polynomial. \\ \\ \\ x^3+ax^2+bx+c \\ \\ \Rightarrow\ x^3-3x^2+0x+4 \\ \\ \Rightarrow\ \bold{x^3-3x^2+4}$

       

$Hope this helps you. \\ \\ Please mark it as the \ \bold{brainliest}\ if this helps. \\ \\ The answer is on my own words, and not from any source. \\ \\ Also, please ask me if you've any doubts.$

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Answer 2

Answer:

x³ - 3x² + 4

Step-by-step explanation:

Let the zeroes be a,b,c.

(i) a + b + c = 3.

(ii) ab + bc + ca = 0

(iii) abc = -4

Therefore, the cubic polynomial is:

⇒ x³ - (a + b + c)x² + (ab + bc + ca)x - abc

⇒ x³ - 3x² + 4

Hope it helps!