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## Answers

Let x = 3

=2(3)³-17(3)²+38(3)-15

=54 - 153 + 114 - 15

=168 - 168

=0

Hence 3 is the zero of the given polynomial.

In the same way,

Let x = 1/2

=2(1/2)³-17(1/2)²+38(1/2)-15

=2(1/8) - 17(1/4) + 19 - 15

= 1/4 - 17/4 + 4

= -16/4 + 4

= -4 + 4

=0

Hence 1/2 is the zero of the given polynomial.

then x = 1/2 and 3.

When x = 1/2,

p(x) = 2*(1/2)³ - 17* (1/2)² + 38* 1/2 - 15

=> 2*1/8 - 17*1/4 + 38/2 -15

=>1/4 - 17/4 + 19 -15

=>

__1-17__+ 4

__4__

=>

__-16 + 16__

4

__=>__

__0__

4

=> 0

The value of the polynomial is 0. Therefore 1/2 is a zero of the polynomial.

If x = 3,

then p(x) = 2*(3)³ - 17* (3)² + 38*3 -15

⇒2*27 - 17* 9 +114 - 15

⇒54 - 153 + 114 - 15

⇒54 +114 - 153 - 15

⇒168 - 168

⇒0

The value is 0, therefore 3 is the zero of a polynomial.