Find a quadratic polynomial whose sum and product of its zeroes are 2 + root3 and 1/2-root3 - Maths - Polynomials

Question

Find a quadratic polynomial whose sum and product of its zeroes
are 2 + root3 and 1/2-root3

Ajanta Trivedi · Accepted Answer

sum of the zeroes = $2 + \sqrt{3}$ and

product of zeroes = $\frac{1}{2 - \sqrt{3}}$ now rationalising the denominator:

$\frac{1}{2 - \sqrt{3}} = \frac{1}{2 - \sqrt{3}} * \frac{2 + \sqrt{3}}{2 + \sqrt{3}} = \frac{2 + \sqrt{3}}{4 - 3} = 2 + \sqrt{3}$

thus product of zeroes = $2 + \sqrt{3}$

quadratic polynomial = $x^{2} - x (s u m o f z e r o e s) + p r o d u c t o f z e r o e s$

$= x^{2} - x (2 + \sqrt{3}) + 2 + \sqrt{3}$

hope this helps you.

cheers!!