843/VB02. problem / Math - Solved Math Problems

MR-843 / 423a. 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:

$x^{2} - 5 x + 6 = 0$

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

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

$x^{2} - 5 x + 6 = 0$

$a = 1; b = - 5; c = 6$

$x_{1, 2} = \frac{- (- 5) \pm \sqrt{{(- 5)}^{2} - 4 \cdot 1 \cdot 6}}{2 \cdot 1}$

$x_{1, 2} = \frac{5 \pm \sqrt{25 - 24}}{2}$

$x_{1, 2} = \frac{5 \pm \sqrt{1}}{2}$

$x_{1, 2} = \frac{5 \pm 1}{2}$

$x_{1} = \frac{5 + 1}{2} = \frac{6}{2}$

$x_{1} = 3$

$x_{2} = \frac{5 - 1}{2} = \frac{4}{2}$

$x_{2} = 2$

$x_{1} = 3; x_{2} = 2$

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