Question

construct the quadratic equation whose roots are root 3 and root 3

Answer 1

Answer:

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

Answer 2

Answer:

$Required\: Quadratic\: equation:\\x^{2}-2\sqrt{3}x+3=0$

Step-by-step explanation:

$Let\: \alpha \:and \: \beta \\are \: two \: roots \: of \:a \\quadratic\: equation.$

$\alpha = \sqrt{3}\\\beta =\sqrt{3}\:(given)$

$Form \:of\:a\: Quadratic\\equation \:whose\:roots \:are\\\alpha \:\beta \:is$

$x^{2}-(\alpha+\beta)x+\alpha\beta=0$

$\implies x^{2}-(\sqrt{3}+\sqrt{3})x+\sqrt{3}\times \sqrt{3}=0$

$\implies x^{2}-2\sqrt{3}x+3=0$

Therefore,

$Required\: Quadratic\: equation:\\x^{2}-2\sqrt{3}x+3=0$

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