Question

If x = 1 by 3 is zero polynomial p x equal to 27 x cube minus ax square minus x + 3 then find the value of a

Answer 1

Step-by-step explanation:

$</p><p>a = 33 \\ </p><p></p><p></p><p> </p><p>x = \frac{1}{ 3} \\ p(x) = 27 {x}^{3} - a {x}^{2} - x + 3 \\ p( \frac{1}{3}) = 27 \times \frac{1}{3}^{3} - a \times \frac{1}{3}^{2} - \frac{1}{3} + 3 \\ \: \: \: \: \: = 27 \times \frac{1}{27} - \frac{a}{9} - \frac{1}{3} + 3 = 0 \\ \: \: \: \: = 1 - \frac{a}{9} - \frac{1}{3} + \frac{9}{3} = 0 \\ \: \: \: = \frac{3}{3} - \frac{1}{3} + \frac{9}{3} - \frac{a}{9} = 0 \\ \: \: \: \: \: = \frac{11}{3} - \frac{a}{9} = 0 \\ \: \: \: = - \frac{a}{9 } = - \frac{11}{3 } \\ \: \: \: \: = - a = \frac{ - 11}{3} \times 9 \\ \: \: \: \: \: = - a = - 11 \times 3 = - 33 \\ a = 33$

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