Question

Find a quadratic polynomial whose zeroes are (2+root5÷2) and (2-root5) ÷2

Answer 1

${x}^{2} - ((2 + \sqrt{5 })/2 + (2 - \sqrt{5})/2 )x +(( 2 - \sqrt{5} )/2)((2 + \sqrt{5})/2 ) = 0 \\ implies \: {x}^{2} + x - 1/4 = 0$

we know that if a and b be the zeros of the quadratic polynomial then equation of polynomial is written as

${x}^{2} - (a + b)x + ab = 0$