Question

find the quadratic equation whose roots are 2 + root 3 and 2- root 3

Answer 1

Here is the answer...

Answer 2

Answer:

The quadratic equation whose roots are (2+√3) and (2-√3) is x²-4x+1=0

Step-by-step explanation:

Let the quadratic equation be

ax²+bx+c=0, a≠0 and

$it's \: zeroes\:be\: \alpha \\ and \: \beta .$

$Here, \alpha =2+\sqrt{3},and\:\beta = 2-\sqrt{3}$

$Sum \:of \: the \: roots \\= \alpha+\beta\\=2+\sqrt{3}+2-\sqrt{3}\\=4$

$Product \:of \: the \: roots \\= \alpha \beta\\=(2+\sqrt{3})(2-\sqrt{3})\\=2^{2}-(\sqrt{3})^{2}\\=4-3\\=1$

Therefore,

The quadratic equation is ax²+bx+c =0 is

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

$\implies x^{2}-4x+1=0$

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