QQuestion
Solve the following quadratic equation for x and give your answers correct to three significant figures:
2x² − 10x + 5 = 0
✓Answer
Comparing 2x² − 10x + 5 = 0 with ax² + bx + c = 0:
a = 2, b = −10 and c = 5
Using the quadratic formula:
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}Substituting the values:
x=\frac{-(-10)\pm\sqrt{(-10)^2-4(2)(5)}}{2(2)}⇒ x=\frac{10\pm\sqrt{100-40}}{4}
⇒ x=\frac{10\pm\sqrt{60}}{4}
⇒ x=\frac{10\pm2\sqrt{15}}{4}
⇒ x=\frac{5\pm\sqrt{15}}{2}
Since √15 ≈ 3.87298:
x = (5 + 3.87298)/2 or x = (5 − 3.87298)/2
⇒ x ≈ 4.43649 or x ≈ 0.563508
Correct to three significant figures:
x = 4.44 or x = 0.564
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