Question

Find a quadratic polynomial , the sum of whose zeros is 11 and one zero is 6

Answer 1

$Sum \: of \: zeroes = \: (\alpha + \beta) \: = 11 \\ one \: zero \: is \: given \: \\ let \: \alpha = 6 \\ then \: \beta = 11 - 6 = 5 \: \: \\ Product \: of \: zeroes = \: \alpha \beta =6 \times 5 = 30 \\ For \: quadratic \: equation \: \\ x^2 -(Sum\: of \: zeroes)x +(Product \: of \: zeroes) = 0 \\ x ^{2} - 11x + 30 = 0 \\so \: the \: quadratic \: polynomial \: is \: x ^{2} - 11x + 30$