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Mathematics

Solve the following equation using quadratic formula:

5x2 - 19x + 17 = 0

Quadratic Equations

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Answer

Comparing equation 5x2 - 19x + 17 = 0 with ax2 + bx + c = 0, we get :

a = 5, b = -19 and c = 17.

By formula,

x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values we get :

⇒x=−(−19)±(−19)2−4×5×172×5=19±361−34010=19±2110=19+2110 or 19−2110.\Rightarrow x = \dfrac{-(-19) \pm \sqrt{(-19)^2 - 4 \times 5 \times 17}}{2 \times 5} \\[1em] = \dfrac{19 \pm \sqrt{361 - 340}}{10} \\[1em] = \dfrac{19 \pm \sqrt{21}}{10} \\[1em] = \dfrac{19 + \sqrt{21}}{10} \text{ or } \dfrac{19 - \sqrt{21}}{10}.

Hence, x={19+2110,19−2110}x = \Big{\dfrac{19 + \sqrt{21}}{10}, \dfrac{19 - \sqrt{21}}{10}\Big}.

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