848/VB02. problem / Math - Solved Math Problems

MR-848 / 423e. 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:

$4 x^{2} - 17 x + 4 = 0$

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

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

$4 x^{2} - 17 x + 4 = 0$

$a = 4; b = - 17; c = 4$

$x_{1, 2} = \frac{- (- 17) \pm \sqrt{{(- 17)}^{2} - 4 \cdot 4 \cdot 4}}{2 \cdot 4}$

$x_{1, 2} = \frac{17 \pm \sqrt{289 - 64}}{8}$

$x_{1, 2} = \frac{17 \pm \sqrt{225}}{8}$

$x_{1, 2} = \frac{17 \pm 15}{8}$

$x_{1} = \frac{17 + 15}{8} = \frac{32}{8}$

$x_{1} = 4$

$x_{2} = \frac{17 - 15}{8} = \frac{2}{8}$

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

$x_{1} = 4; x_{2} = \frac{1}{4}$

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