Question

Find all zeroes of p(x)=3x^2-5 and verify relationships. Also find a polynomial whose zeroes are reciprocal of the zeroes of p(x).

Answer 1

${3x}^{2} - 5 = 0 \\ {3x}^{2} = 5 \\ {x}^{2} = \frac{3}{5} \\ x = \sqrt{ \frac{3}{5} } \: \: or \: \: - \sqrt{ \frac{3}{5} } \\ \\ their \: reciprocals \: are \\ \\ x = \sqrt{ \frac{5}{3} } \: or \: - \sqrt{ \frac{5}{3} } \\ \\ sum \: of \: roots \: is \: 0 \\ \\ product \: of \: roots \: is - \frac{5}{3} \\ so \: polynomial \: having \: roots \: given \: is \: \\ \\ p(x) = {x}^{2} - \frac{5}{3} \: or \: p(x) = {3x}^{2} - 5$

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