Question

what is the quadratuc equation of roots is 2+√3 and 2-√3​

Answer 1

HEY MATE HERE IS YOUR ANSWER...................

Let α = 2+√3

and β = 2-√3

sum of zeroes = α+β = 2+ √3 + 2-√3 = 4

product of zeroes = αβ = (2+√3)(2-√3)= 2-3 = -1

Quadratic equation= x² - (sum of zeroes)x + (product of zeroes)

                                = x² - 4x - 1

Hence, required quadratic equation is x²- 4x - 1

HOPE IT HELP YOU.........................:)

Answer 2

Answer:

$let \: 2 + \sqrt{3} is \: \alpha \: and \: 2 - \sqrt{3} is \: \beta \\ sum \: of \: zeroes = 2 + \sqrt{3} + 2 - \sqrt{3} = 4 \\ product \: of \: zeroes = (2 + \sqrt{3} )(2 - \sqrt{3} ) \\ = 4 - 2 \sqrt{3} + 2 \sqrt{3} - 3 = 1 \\ general \: form \: of \: quadratic \: {eq}^{2} \\ = a {x}^{2} +bx + c = 0\\ a( {x}^{2} + \frac{b}{a} x + \frac{c}{a} ) = 0 \\ {x}^{2} + \frac{b}{a} x + \frac{c}{a} = 0 \\ {x}^{2} - (sum \: of \: zeroes) + (product \: of \: zeroes) = 0 \\ \bold{ {x}^{2} - 4x + 1}$

so, x²-4x+1 us the quadratic equation whose zeroes are 2+√3 and 2-√3

hope it helps you.....