Which constant should be added and subtracted to solve the quadratic equation 4x² - √3x - 5= 0, by the method of completing the square?
(a) 9/17
(b) 3/16
(c) 3/4
(d) √3/4
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Answered by
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Answer:
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Answered by
2
Answer:
(b) 3/16
Step-by-step explanation:
For ax² + bx + c = 0, to complete the square youl want to add/subtract b²/4a.
Here, we have 4x² - √3x - 5 = 0, so a = 4 and b = -√3. This means we need to add/subtract 3/16.
Going beyond the question asked...
When you do this, you get...
4x² - √3x - 5 = 0
⇒ (4x² - √3x + 3/16) - 3/16 - 5 = 0
⇒ (2x - √3 / 4)² = 3/16 + 5 = 83 / 16
⇒ 2x - √3 / 4 = ±√83 / 4
⇒ 2x = (√3 ± √83) / 4
⇒ x = (√3 ± √83) / 8
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