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ICSEClass 10MathematicsQuadratic Equations04 Mark2023 Easy

QQuestion

Solve the following quadratic equation:

x2 + 4x − 8 = 0.

Give your answer correct to one decimal place. Use mathematical tables if necessary.

Exam-ready answer • 04 Mark

Answer

Comparing x2 + 4x − 8 = 0 with ax2 + bx + c = 0:

a = 1, b = 4 and c = −8.

Using the quadratic formula:

⇒ x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

⇒ x = \frac{-4\pm\sqrt{4^2-4(1)(-8)}}{2(1)}

⇒ x = \frac{-4\pm\sqrt{16+32}}{2}

⇒ x = \frac{-4\pm\sqrt{48}}{2}

⇒ x = \frac{-4\pm4\sqrt{3}}{2}

⇒ x = -2\pm2\sqrt{3}

Using √3 = 1.732:

x = −2 ± 2(1.732)

x = −2 ± 3.464

x = −2 + 3.464 or x = −2 − 3.464

x = 1.464 or x = −5.464

Correct to one decimal place, x = 1.5 or x = −5.5.

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