Question

alpha and beta are the zero of 4x2-1 then alpha2+ beta2​

Answer 1

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$\alpha \: \: and \: \: \beta \: \: are \: the \: zeroes \: of \: this \: \: \\ polynomial \\ 4 {x}^{2} - 1 \\ \\ \therefore \: \: \alpha + \beta = 0 \: \: and \\ \alpha \beta = - \frac{1}{4} \\ \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ \: \: \: \: \: \: \: = {0}^{2} - 2 \times - \frac{1}{4} \\ \: \: \: \: \: \: \: \: \: \: = \frac{1}{2}$

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