QQuestion
Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.
✓Answer
Comparing 2x² − 5x − 4 = 0 with ax² + bx + c = 0:
a = 2, b = −5 and c = −4.
Using the quadratic formula:
x = \frac{-\mathrm{b}\pm\sqrt{\mathrm{b}^2-4ac}}{2\mathrm{a}}
x = \frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-4)}}{2(2)}
⇒ x = \frac{5\pm\sqrt{25+32}}{4}
⇒ x = \frac{5\pm\sqrt{57}}{4}
Since √57 ≈ 7.54983:
x = (5 + 7.54983)/4 or x = (5 − 7.54983)/4
⇒ x ≈ 3.13746 or x ≈ −0.637458
Correct to three significant figures:
x = 3.14 or x = −0.637
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