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Mathematics

Solve the following quadratic equation :

x2 + 4x - 8 = 0.

Give your answer correct to one decimal place.

Quadratic Equations

ICSE 2023

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Answer

Comparing x2 + 4x - 8 = 0 with ax2 + bx + c, we get :

a = 1, b = 4 and c = -8.

By formula,

⇒x=−b±b2−4ac2a=−4±42−4×1×(−8)2×1=−4±16+322=−4±482=−4±432=−2±23=−2±2×1.732=−2±3.464=−2+3.464 or −2−3.464=1.464 or −5.464=1.5 or −5.5\Rightarrow x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[1em] = \dfrac{-4 \pm \sqrt{4^2 - 4 \times 1 \times (-8)}}{2 \times 1} \\[1em] = \dfrac{-4 \pm \sqrt{16 + 32}}{2} \\[1em] = \dfrac{-4 \pm \sqrt{48}}{2} \\[1em] = \dfrac{-4 \pm 4\sqrt{3}}{2} \\[1em] = -2 \pm 2\sqrt{3} \\[1em] = -2 \pm 2 \times 1.732 \\[1em] = -2 \pm 3.464 \\[1em] = -2 + 3.464 \text{ or } -2 - 3.464 \\[1em] = 1.464 \text{ or } -5.464 \\[1em] = 1.5 \text{ or } -5.5

Hence, x = 1.5 or 5.5

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