Question

check whether 2,3and ½ are the zeros of polynomial p (x) = 2x³-11x² +17x-6

Answer 1

HEYA!!!!

Here is your answer :
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Given,

Zeroes = 2,3,1/2

Verification :
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$p(x) = 2 {x}^{3} - 11 {x}^{2} + 17x - 6 \\ \\ p(2) = 2 {(2)}^{3} - 11 {(2)}^{2} + 17(2) - 6 \\ \\ p(2) = 2(8) - 11(4) + 34 - 6 \\ \\ p(2) = 16 - 44 + 34 - 6 \\ \\ p(2) = 50 - 50 \\ \\ p(2) = 0$

It is a zero.

ii)
$p(x) = 2 {x}^{3} - 11 {x}^{2} + 17x - 6 \\ \\ p(3) = 2 {(3)}^{2} - 11 {(3)}^{2} + 17(3) - 6 \\ \\ p(3) = 2(9) - 11(9) + 51 - 6 \\ \\ p(3) = 18 - 99 + 51 - 6 \\ \\ p(3) = 69 - 105 \\ \\ p(3) = - 36$

It is not a zero.

iii)
$p( \frac{1}{2} ) = 2( { \frac{(1)}{(2)} }^{2} ) - 11 {( \frac{1}{2)} }^{2} + 17( \frac{1}{2} ) - 6 \\ \\ p( \frac{1}{2} ) = 2( \frac{1}{4} ) - 11( \frac{1}{2} ) + \frac{17}{2} - 6 \\ \\ p( \frac{1}{2} ) = \frac{1}{2} - \frac{11}{2} + \frac{17}{2} - 6 \\ \\ p( \frac{1}{2)} = \frac{18}{2} - \frac{11}{2} - 6 \\ \\ p( \frac{1}{2} ) = \frac{7}{2} - 6 \\ \\ p( \frac{1}{2} ) = - \frac{5}{2}$

It is not a zero.

HOPE THIS HELPS U...