Question

Find a quadratic polynomial with sum of zeroes 2+√3 and product of zeroes 2+√3

Answer 1

Hi friend,

Let the alpha = 2+✓3 and Beta = 2+✓3

Sum of zeros = (Alpha + Beta) = (2+✓3+2+✓3) = 4+2✓3.

Product of zeros = (Alpha×Beta) = (2+✓3)(2+✓3) = (2+✓3)² = (2)² + (✓3)² + 2 × 2 × ✓3 = 4 + 3 + 4✓3 = 7+4✓3.


Therefore,


The required polynomial = X²-(Alpha+Beta)X+Alpha × Beta.

=> X²-(4+2✓3)X+7+4✓3

=> X²-4X-2✓3X+7+4✓3.


HOPE IT WILL HELP YOU.... :-)