Question

write the quadratic equation formed by the roots​

Answer 1

$\huge{\mathcal{\blue{\underline{Answer}}}}$

Given that the roots ➡ 3+√5,3-√5

let the roots of the quadratic equation be x ,

$x = 3 + \sqrt{5} \\ x - 3 - \sqrt{5} = 0........(1)$

$x = 3 - \sqrt{5} \\ x - 3 + \sqrt{5} = 0 .........(2)$

Multiplying (1) and (2) , we get

$(x - 3 - \sqrt{5} )(x - 3 + \sqrt{5} ) = 0 \\ (x - 3) {}^{2} - ( \sqrt{5} ) { }^{2} = 0 \\ x {}^{2} + 9 - 6x - 5 = 0 \\ x {}^{2} - 6x + 4 = 0$