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Solve the equation 3x2 - 4x - 4 = 0 by using formula giving answer correct to three decimal places.

Quadratic Equations

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Answer

Comparing equation, 3x2 - 4x - 4 = 0 with ax2 + bx + c = 0.

a = 3, b = -4 and c = -4.

By formula,

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

Substituting values we get :

⇒x=−(−4)±(−4)2−4×3×(−4)2×3⇒x=4±16+486⇒x=4±646⇒x=4±86⇒x=4+86,4−86⇒x=126,−46⇒x=2,−23⇒x=2.000,−0.667.\Rightarrow x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 3 \times (-4)}}{2 \times 3} \\[1em] \Rightarrow x = \dfrac{4 \pm \sqrt{16 + 48}}{6} \\[1em] \Rightarrow x = \dfrac{4 \pm \sqrt{64}}{6} \\[1em] \Rightarrow x = \dfrac{4 \pm 8}{6} \\[1em] \Rightarrow x = \dfrac{4 + 8}{6}, \dfrac{4 - 8}{6} \\[1em] \Rightarrow x = \dfrac{12}{6}, \dfrac{-4}{6} \\[1em] \Rightarrow x = 2, -\dfrac{2}{3} \\[1em] \Rightarrow x = 2.000, -0.667.

Hence, x = 2.000, -0.667.

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