Question

the quadratic polynomial whose zeroes are tan30° tan60°​

Answer 1

Zeroes are = tan 30° and tan 60°

tan 30° = 1/√3 and tan 60° = √3

Sum of zeroes = 1/√3 + √3

==> 1 + 3 / √3

sum of zeroes = 4/√3

Product of zeroes = 1/√3 × √3

Product of zeroes = 1

p(x) = x² - ( sum of zeroes)x + ( product of zeroes )

==> p(x) = x² - 4/√3 x + 1

Multiply by √3

==> p(x) = √3x² - 4x + √3