Question

- Find the quadratic equations whose roots are the
reciprocals of the roots of 2x2+ 5x + 3 = 0.

Answer 1

${2x}^{2} + 5x + 3 = 0 \\ {2x}^{2} + 3x + 2x + 3 = 0 \\ x(2x + 3) + 1(2x + 3) \\ (x + 1) \: (2x + 3) \\ x = - 1 \\ x = \frac{3}{2} \\ \\ we \: have \: to \: find \: a \: quadratic \: equations \: whose \: zeros \: are \: reciprocals \: of \: these \: zeros \: \\ the \: formula \: to \: make \: a \: quadratic \: equation \: is \\ {x}^{2} - (a + b)x + (a \times b) \\ where \: a \: and \: b \: are \: the \: alpha \: and \: beta \\ now \: \\ {x}^{2} + \frac{1}{3}x + - \frac{3}{2}$

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