Question

. Find a quadratic polynomial whose zeroes are 7-√2 and 7+√2
answer fastly

Answer 1

$\textbf{Given:}$

$\textsf{Zeroes are}$

$\mathsf{7-\sqrt{2}\;and\;7+\sqrt{2}}$

$\textbf{To find:}$

$\textsf{A quadratic polynomial whose zeroes are}$

$\mathsf{7-\sqrt{2}\;and\;7+\sqrt{2}}$

$\textbf{Solution:}$

$\underline{\textbf{Sum of the zeroes:}}$

$\mathsf{=7-\sqrt{2}+7+\sqrt{2}}$

$\mathsf{=14}$

$\underline{\textbf{Product of the zeroes:}}$

$\mathsf{=(7-\sqrt{2})(7+\sqrt{2})}$

$\mathsf{=7^2-\sqrt{2}^2}$

$\mathsf{=49-2}$

$\mathsf{=47}$

$\therefore\textsf{The required plynomial is}$

$\mathsf{x^2-(sum\;of\;the\;zeroes)x+product\;of\;the\;zeros}$

$\implies\boxed{\mathsf{x^2-14x+47}}$

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