Question

Form a quadratic polynomial whose zeros
are 7+2√2and 7-2√2​

Answer 1

Answer:

k[x^2-14x+41]

Step-by-step explanation:

general form of equation =

k[x^2-(sum of zeroes)+(product of zeroes)

sum of zeroes = 7+2√2 +7-2√2 =14

product of zeroes=(7+2√2)(7-2√2)=41

Answer 2

Answer:

$\large \mathsf{ Quadratic \: polynomial⇒ {x}^{2} - 14x + 41}$

Step-by-step explanation:

$\large \mathtt{ \alpha = 7 + 2 \sqrt{2} \qquad\beta = 7 - 2 \sqrt{2} }$

$\mathtt{ :⟹\alpha + \beta = 7 + 2 \sqrt{2} + 7 - 2 \sqrt{2} }$

$\large\mathtt { \boxed{ \boxed{ \color{aqua}{:⟹\alpha + \beta = 14} }}}$

$\mathtt{:⟹ \alpha \times \beta = (7 + 2 \sqrt{2}) (7 - 2 \sqrt{2} )}$

$\mathtt{ :⟹\alpha \times \beta = 49 - 8 }$

$\large \mathtt{ \boxed{ \boxed {\color{aqua}{ :⟹\alpha \times \beta = 41}}}}$

$\mathsf{General \: form \: of \: quadratic \: equation:}$

$\mathtt{ \bold{ \underline{:⟹{x}^{2} - ( \alpha + \beta )x + (\alpha \times \beta )}}}$

$\large\mathtt{ \color{olive}{:⟹ {x}^{2} - 14x + 41}}$

Note:-

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