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Mathematics

Solve the following quadratic equation 2x2 − 5x − 4 = 0. Give your answer correct to three significant figures.

Quadratic Equations

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Answer

Given,

⇒ 2x2 − 5x − 4 = 0

Comparing equation 2x2 − 5x − 4 = 0 with ax2 + bx + c = 0, we get :

a = 2, b = -5 and c = -4.

By formula,

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

Substituting values we get :

⇒x=−(−5)±(−5)2−4×(2)×(−4)2×(2)=5±25−(−32)4=5±25+324=5±574=5+574 or 5−574=5+7.554 or 5−7.554=12.554 or −2.554=3.14 or −0.638\Rightarrow x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4 \times (2) \times (-4)}}{2 \times (2)} \\[1em] = \dfrac{5 \pm \sqrt{25 - (-32)}}{4} \\[1em] = \dfrac{5 \pm \sqrt{25 + 32}}{4} \\[1em] = \dfrac{5 \pm \sqrt{57}}{4} \\[1em] = \dfrac{5 + \sqrt{57}}{4} \text{ or } \dfrac{5 - \sqrt{57}}{4} \\[1em] = \dfrac{5 + 7.55}{4} \text{ or } \dfrac{5 - 7.55}{4} \\[1em] = \dfrac{12.55}{4} \text{ or } \dfrac{-2.55}{4} \\[1em] = 3.14 \text{ or } -0.638

Hence, x = 3.14, -0.638.

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