Question

Verify that 3 is the zero of the cubic polynomial p(x) = 3x^3-5x^2-11x-3

Answer 1

if 3 is a zero of the polynomial p(x),

then p(3) will be equal to zero.

then

p(3)=3×(3)³-5×(3)²-11×3-3,

p(3)=3×27-5×9-33-3,

p(3)=81-45-36,

p(3)=81-81,

p(3)=0,

since
p(3)=0,

therefore

3 is a zero of the polynomial.

Answer 2

Hey mate, here is your answer -:)

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$p(x) = {3x}^{3} - {5x}^{2} - 11x - 3 \\ \\ on \: putting \: x = 3 \\ \\ p(3) = 3 {(3)}^{3} - 5 {(3)}^{2} - 11(3) - 3 \\ \: \: \: \: \: \: \: \: \: = 3(27) - 5(9) - 11(3) - 3 \\ \: \: \: \: \: \: \: \: \: = 81 - 45 - 33 - 3 \\ \: \: \: \: \: \: \: \: \: = 81 - 81 \\ \: \: \: \: \: \: \: \: \: = 0$

$hence \: verified....$


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HOPE it helps to you!!!