Question

Determine weather the given value of x is zero of the given polynomial or not 2x^2 -6x+ 3,x=1\2

Answer 1

We have given

$p(x) = 2 {x}^{2} - 6x + 3$

$x = \frac{1}{2}$
For zeroes , f(1/2) should be equal to 0.

$i.e.. \: f( \frac{1}{2} ) = 0$

So putting the value of x in p(x), we get

$p (\frac{1}{2} ) = 2 {( \frac{1}{2}) }^{2} - 6( \frac{1}{2} ) + 3 \\ \\ \: \: \: \: \: \: \: \: \: = 2( \frac{1}{4} ) - 3 + 3 \\ \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} - 3 + 3 \\ \\ \: \: \: \: = \frac{1}{2}$

As 1/2 is not equal to 0.

or p(1/2) is not equal to 0.

so, 1/2 is not a zero of the given p(x).