Which constant should be added and substracted to solve the quadratic

1.	Which constant should be added and substracted to solve the quadratic equation 4x2 – √3x – 5 = 0 by the method of completing the square?A) 3/16B) √3/4C) 9/16D) 3/4
Answer» Correct option is (A) 3/16 Given equation is \(4x^2-\sqrt{3}x-5=0\) \(\Rightarrow(2x)^2-2\times2x\times\frac{\sqrt{3}}4-5=0\) \((\because2\times2x\times\frac{\sqrt{3}}4=\sqrt3x)\) \(\Rightarrow(2x)^2-2\times2x\times\frac{\sqrt3}4\) \(+(\frac{\sqrt3}4)^2-5-(\frac{\sqrt3}4)^2=0\) \(\Rightarrow(2x-\frac{\sqrt3}4)^2-(5+\frac3{16})=0\) Thus, we have to add or subtract \(\frac{3}{16}\) to solve the given quadratic equation by the method of completing the square. Correct option is A) 3/16

Which constant should be added and substracted to solve the quadratic equation 4x2 – √3x – 5 = 0 by the method of completing the square?A) 3/16B) √3/4C) 9/16D) 3/4

Answer»

Correct option is (A) 3/16

Given equation is \(4x^2-\sqrt{3}x-5=0\)

\(\Rightarrow(2x)^2-2\times2x\times\frac{\sqrt{3}}4-5=0\) \((\because2\times2x\times\frac{\sqrt{3}}4=\sqrt3x)\)

\(\Rightarrow(2x)^2-2\times2x\times\frac{\sqrt3}4\) \(+(\frac{\sqrt3}4)^2-5-(\frac{\sqrt3}4)^2=0\)

\(\Rightarrow(2x-\frac{\sqrt3}4)^2-(5+\frac3{16})=0\)

Thus, we have to add or subtract \(\frac{3}{16}\) to solve the given quadratic equation by the method of completing the square.

Correct option is A) 3/16