Question

if a, B and y are the zeroes of the polynomial x3 + x2 - 2x +3, then the value
of a2 + B2 + y² is equal to​

Answer 1

$\underline{\textbf{Given:}}$

$\text{\boldmath \alpha,\beta\;and\;\gamma\;are\;zeroes\;of\;x^3+x^2-2x+3 }$

$\underline{\textbf{To find:}}$

$\textsf{The value of}$

$\text{\boldmath \alpha^2+\beta^2+\gamma^2 }$

$\underline{\textbf{Solution:}}$

$\text{\boldmath \alpha,\beta\;and\;\gamma\;are\;zeroes\;of\;x^3+x^2-2x+3 }$

$\mathsf{Then,}$

$\text{\boldmath \alpha+\beta+\gamma=-1 }$

$\text{\boldmath \alpha\beta+\beta\gmma+\gamma\alpha=2 }$

$\text{\boldmath \alpha\beta\gamma=-3 }$

$\mathsf{Consider}$

$\text{\boldmath \alpha^2+\beta^2+\gamma^2 }$

$\text{=\boldmath (\alpha+\beta+\gamma)^2-2(\alpha\beta+\beta\gmma+\gamma\alpha) }$

$\mathsf{=(-1)^2-2(2)}$

$\mathsf{=1-4}$

$\mathsf{=-3}$

$\implies\boxed{\text{\boldmath \alpha^2+\beta^2+\gamma^2=-3 }}$

$\underline{\textbf{Find more:}}$