Question

Alpha and beta are the zeros of polynomial fx equal to x square - 6 x + k then find the value of k such that alpha square + beta square is equal to 40

Answer 1

${x}^{2} - 6x + k \\ \alpha + \beta = 6 \\ \alpha \beta = k \\ { \alpha }^{2} + { \beta }^{2} = 40 \\ \\ { ( \alpha + \beta )}^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta \\ 36 = 40 + 2k \\ 2k = - 4 \\ k = - 2$
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