Question

find all zeros of the quadratic polynomial the sum and product of whose zeros are 6 and 9 respectively hence find the zeros

Answer 1

$Sum \: of \: zeroes = \: (\alpha + \beta) \: = 6 \\ Product \: of \: zeroes = \: \alpha \beta = \: 9 \\ For \: quadratic \: equation \\ \: x^2 -(Sum\: of \: zeroes)x +(Product \: of \: zeroes) = 0 \\ x ^{2} - 6x + 9= 0 \\ x ^{2} -3 x - 3x + 9 = 0 \\ x(x - 3) - 3(x - 3) = 0 \\ (x - 3)(x - 3) = 0 \\ x - 3 = 0 \\ x = 3 \\ and \\ x - 3 = 0 \\ x = 3$