A quadratic equation

#quadratic equation#discriminant#roots

Statement

Solve in $\mathbb{R}$ the equation
$2x^2-5x+2=0.$

Hint

Compute the discriminant $\Delta=b^2-4ac$ .

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Discriminant. $\Delta=(-5)^2-4\cdot2\cdot2=25-16=9$ .

Roots. $\sqrt\Delta=3$ , so
$x_1=\frac{5-3}{4}=\frac12, \qquad x_2=\frac{5+3}{4}=2.$

Conclusion. $x\in\{1/2,\,2\}$ .