Math, asked by anirudhvarma513, 10 months ago

answer it please it is very important

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Answered by abhinay365

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$\boxed{Answer:-}$

Given

$p(x) = 3 {x}^{2} - 5x - 2$

Given numbers are

$2 \: and \: \frac{ - 1}{3}$

Now

$p(2) = 3 ({2})^{2} - 5(2) - 2 \\ = 3 \times 4 - 5 \times 2 - 2 \\ = 12 - 10 - 2 \\ = 12 - 12 = 0 \\ p( 2) = 0$

And

$p( \frac{ - 1}{3} ) = 3 { (\frac{ - 1}{3} )}^{2} - 5( \frac{ - 1}{3} ) - 2 \\ = 3 \times \frac{1}{9} + 5 \times \frac{1}{3} - 2 \\ = \frac{1}{3} + \frac{5}{3} - 2 \\ = \frac{1 +5 - 2 \times 3}{3} \\ = \frac{1 + 5 - 6}{3} \\ = \frac{6 - 6}{3} \\ = \frac{0}{3} = 0 \\ p( \frac{ - 1}{3} ) = 0$

Hence the given numbers are the roots of the polynomial.

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Abhinay

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