Which constant must be added and subtracted to solve the quadratic equation 9x^2 + 3x – 8 = 0
Which constant must be added and subtracted to solve the quadratic equation 9x2 + 3x – 8 = 0 by the method of completing the square ?
A) 1/36
B) 9/64
C) 1/3
D) 1/4
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Correct option is (D) 1/4
Given quadratic equation is
\(9x^2+3x-8=0\)
\(\Rightarrow(3x)^2+2\times3x\times\frac12+(\frac12)^2-(\frac12)^2-8=0\)
(By adding and subtract \((\frac12)^2\;or\;\frac14\) in L.H.S.)
\(\Rightarrow(3x+\frac12)^2-(8+\frac14)=0\)
\(\Rightarrow(3x+\frac12)^2=\frac{33}4\)
\(\Rightarrow3x+\frac12=\frac{\pm\sqrt{33}}2\)
\(\Rightarrow3x=-\frac12\pm\frac{\sqrt{33}}2\)
\(\Rightarrow x=-\frac16\pm\frac{\sqrt{33}}6\)
Hence, we have to add or subtract \(\frac{1}{4}\) to solve the given quadratic equation by the method of completing the square.
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