Question

find the quadratic polynomial whose zeroes are 3-root3/5 and 3+root3/5

Answer 1

x^2-6x+6

Solution:

Given,

$\alpha = 3 - \sqrt \frac{3}{5} \: \: and \: \beta = 3 + \sqrt{ \frac{3}{5} }$

quadratic polynomial=

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

so,

=x^2 - (3-√3/5+3-√3/5)x + (3-√3/5)(3+√3/5)

= x^2 -(3+3)x + (3)^2-(√3/5)^2

= x^2 - 6x +9 - 3/5

$\frac{5x^2 -5(6x )+(6)}{5}$

= x^2-6x+6(Answer)

=