QQuestion
Solve the following quadratic equation:
x2 + 4x − 8 = 0.
Give your answer correct to one decimal place. Use mathematical tables if necessary.
✓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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