Exercise 540Algebra › PolynomialsHigh schoolAdded 3 Nov 2026

Vieta's formulas for a quadratic

#Vieta#sum and product of roots#quadratic

Statement

Let $x_1,x_2$ be the roots of $2X^2-5X+1=0$ . Compute $x_1+x_2$ , $x_1x_2$ , $x_1^2+x_2^2$ , and $1/x_1+1/x_2$ .

Hint

Vieta: $x_1+x_2=-b/a=5/2$ , $x_1x_2=c/a=1/2$ .

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Vieta. $x_1+x_2=5/2$ , $x_1x_2=1/2$ .

$x_1^2+x_2^2$ . $(x_1+x_2)^2-2x_1x_2=25/4-1=21/4$ .

$1/x_1+1/x_2$ . $(x_1+x_2)/(x_1x_2)=(5/2)/(1/2)=5$ .

Conclusion. Sum $5/2$ , product $1/2$ , sum of squares $21/4$ , sum of reciprocals $5$ .