847/VB02. problem / Math - Solved Math Problems

MR-847 / 423d. problem

Using the formula $x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ for solutions of a quadratic equation $a x^{2} + b x + c = 0$ , solve the equation:

$x^{2} - 0, 11 x + 0, 001 = 0$

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Source: Vene T. Bogoslavov: Collection of Solved Problems #2 - 423.d.)

Algebra → Quadratic equations, inequalities and systems of equations → Quadratic equations

$x^{2} - 0, 11 x + 0, 001 = 0$

$a = 1; b = - 0, 11; c = 0, 001$

$x_{1, 2} = \frac{- (- 0, 11) \pm \sqrt{{(- 0, 11)}^{2} - 4 \cdot 1 \cdot 0, 001}}{2 \cdot 1}$

$x_{1, 2} = \frac{0, 11 \pm \sqrt{0, 0121 - 0, 004}}{2}$

$x_{1, 2} = \frac{0, 11 \pm \sqrt{0, 0081}}{2}$

$x_{1, 2} = \frac{0, 11 \pm 0, 09}{2}$

$x_{1} = \frac{0, 11 + 0, 09}{2} = \frac{0, 2}{2}$

$x_{1} = 0, 1$

$x_{2} = \frac{0, 11 - 0, 09}{2} = \frac{0, 02}{2}$

$x_{2} = 0, 01$

$x_{1} = 0, 1; x_{2} = 0, 01$

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