Question

find the quadratic polynomial whose roots are 3 +√5 and 3 +√5

Answer 1

(3+√5) + (3+√5) = -b/a
6+√10 = -b/a

(3+√5)×(3+√5) = c/a
9+5+6√5 = c/a
14+6√5 = c/a
so the polynomial is x^2 -(6+√10)x+(14+6√5).

Answer 2

please check your question once.This type of zeros occurs in conjugate pair,i. e.3+√5,3-√5.for these zeros the solution is here
$a { x }^{2} + bx + c = 0 \\ {x}^{2} + \frac{b}{a} x + \frac{c}{a} = 0$
now sum of zeros = -b/a
$3 + \sqrt{5} + 3 - \sqrt{5} = 6 = \frac{ - b}{a}$
Multiplication of zeros
$(3 + \sqrt{5} )(3 - \sqrt{5} ) = \frac{c}{a} = 4$
so the polynomial is,place the value in above eq
${x}^{2} - 6x + 4 = 0$