Question

Find a quadratic polynomial with one of its zeros is root 5 and sum of zeros is 4

Answer 1

Step-by-step explanation:

$let \: \alpha \: and \: \beta \: be \: the \: zeros \: of \: the \: required \: polynomial \\ therefore \\ \alpha = \sqrt{5}..... (Given) \\sum \: of \: zeros \\ \alpha + \beta = 4... (Given) \\ hence \\ \beta = 4 - \sqrt{5} \\ product \: of \: zeros \\ \alpha \beta = \sqrt{5} (4 - \sqrt{5} ) \\ now \: required \: polynomial \: is \: \\ p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} - 4x + \sqrt{5} (4 - \sqrt{5} ) \\ = {x}^{2} - 4x + 4 \sqrt{5} - 5$