Question

if alpha and beta are the zeros of p(x) =x²-px+q find alpha²+beta²​

Answer 1

Answer:

HOW TO SOLVE?

${x}^{2} - px + q \: has \: two \: zeros \: \alpha and \: \beta \\ sum \: of \: roots = \frac{ - b}{a} \\ product \: of \: roots = \frac{c}{a} \\ \alpha + \beta = \frac{ - ( - p)}{1} \\ \alpha + \beta = p \\ \alpha \beta = \frac{q}{1} \\ \alpha \beta = q \\ { \alpha }^{2} + { \beta }^{2} = ( \alpha + \beta ) {}^{2} - 2 \alpha \beta \\ \\ put \: the \: value \: of \: \alpha \beta \: and \: \alpha + \beta . \\ { \alpha }^{2} + { \beta }^{2} = ( {p)}^{2} - 2(q) \\ { \alpha }^{2} + { \beta }^{2} = {p }^{2} - 2q$

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