Question

find a quadratic polynomial whose zeroes are
$2 + \sqrt{3 \: \: }$
and 2_
$\sqrt{3 \: plz \: } solve \: this \: problem$
hi happy RAKHSHA BHANDHAN to all my friends. ..

Answer 1

I think this is the answer. hope it helps. happy Rakshabandhan.

Answer 2

We have, a=2+√3 and b=2-√3

We know that an quadratic polynomial is of the form,
$p(x) = {x}^{2} - (a + b)x + ab \\ = {x}^{2} - (2 + \sqrt{3} + 2 - \sqrt{3} )x + (2 + \sqrt{3} )(2 - \sqrt{3}) \\ = {x}^{2} -4x + ({2}^{2} - {( \sqrt{3}) }^{2} ) \\ = {x}^{2} - 4x + 4 - 3 \\ = {x}^{2} - 4x + 1$
Hence the quadratic polynomial is
${x}^{2} - 4x + 1$
.

*I have used a instead of alpha and b instead of beta.