$If x = \frac{1}{3} is a solution of the equation a x^{2} + (a - 1) x + 4 = a, find the value of a$

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Solution

The correct option is C

$G i v e n x = \frac{1}{3} a n d a x^{2} + (a - 1) x + 4 = a \Rightarrow a \times {(\frac{1}{3})}^{2} + (a - 1) \frac{1}{3} + 4 = 0 \Rightarrow \frac{a}{9} + \frac{a - 1}{3} + 4 = a \Rightarrow \frac{a + 3 a - 3 + 36}{9} = a \Rightarrow 4 a + 33 = 9 a \Rightarrow - 5 a = - 33 \Rightarrow a = \frac{33}{5} = 6 \frac{3}{5}$

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