Math, asked by harshitgupta4242, 11 months ago

form the quadratic equation whose roots are √3 and 3√3

Answers

Answered by Anonymous

7

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form the quadratic equation whose roots are √3 and 3√3

$\texttt{Answer}$

Given,

$\alpha = \sqrt{3}$

$\beta = 3 \sqrt{3}$

$sum \: of \: roots( \alpha + \beta ) = \sqrt{3} + 3 \sqrt{3} = 4 \sqrt{3}$

$product \: of \: the \: roots = ( \alpha \beta ) = \sqrt{3} (3 \sqrt{3)}$

Quadratic equation

$k(x {}^{2} - ( \alpha + \beta )x + \alpha \beta )$

$k(x {}^{2} - (4 \sqrt{3)}x + \sqrt{3} (3 \sqrt{3)} )$

$k(x {}^{2} - 4 \sqrt{3}x + 9)$

$let \: k = 1$

$x {}^{2} - 4 \sqrt{3}x+ 9$

Answered by Itsritu

5

Answer:

$\alpha = \sqrt{3}$

$\beta = 3 \sqrt{3}$

$the \: sum \: of \: roots \: ( \alpha + \: \beta ) = \sqrt{3} + 3 \sqrt{3} = 4 \sqrt \: {3} .$

$product \: of \: the \: roots \: = (\alpha \beta ) = \sqrt{3}( \: 3 \sqrt{3} ).$

$quadratic \: equation \:$

$k( {x}^{2} - ( \alpha + \beta ) x \: + \alpha \beta .$

$k( {x}^{2} - 4\sqrt{3} )x \: + \: \sqrt{3}(3 \sqrt{3} ) .$

$k(x {}^{2} - 4 \sqrt{3} + 9.$

$let \: k \: = 1.$

${x}^{2} - 4 \sqrt{3}x \: + 9.$

#answerwithquality #BAL.

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