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Mathematics

Solve the equation 3x2 - x - 7 = 0 and give your answer correct to two decimal places.

Quadratic Equations

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Answer

Comparing equation 3x2 - x - 7 = 0 with ax2 + bx + c = 0, we get :

a = 3, b = -1 and c = -7.

By formula,

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

Substituting values we get :

⇒−(−1)±(−1)2−4×3×(−7)2×3⇒1±1+846⇒1±856⇒1±9.226⇒1+9.226,1−9.226⇒10.226,−8.226⇒1.70,−1.37.\Rightarrow \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 3 \times (-7)}}{2 \times 3} \\[1em] \Rightarrow \dfrac{1 \pm \sqrt{1 + 84}}{6} \\[1em] \Rightarrow \dfrac{1 \pm \sqrt{85}}{6} \\[1em] \Rightarrow \dfrac{1 \pm 9.22}{6} \\[1em] \Rightarrow \dfrac{1 + 9.22}{6}, \dfrac{1 - 9.22}{6} \\[1em] \Rightarrow \dfrac{10.22}{6}, \dfrac{-8.22}{6} \\[1em] \Rightarrow 1.70, -1.37.

Hence, x = 1.70, -1.37

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