Question

How many zeros does the polynomial (x – 3)2 – 4 can have? Also, find its zeroes

Answer 1

Answer:

Answer: the polynomial has 2 zeroes as it is quadratic equation . Since, it is a quadratic polynomial it will have two zeroes

Answer 2

$Given \: polynomial \:p(x) = (x-3)^{2} - 4$

$Degree \: p(x) \: is \: 2 , So, it \:is \:a \\quadratic \: polynomial \:and \: it \:has \: two \\zeroes .$

$Finding \: zeroes \: of \:p(x), is \:the \:same \\as \: solving \: the \: equation \: p(x) = 0$

$As , (x-3)^{2} - 4 = 0$

$\implies (x-3)^{2} - 2^{2} = 0$

$\implies [ (x-3)+2 ][ (x-3) - 2 ] = 0$

$\implies x-3+2 = 0 \:Or \: x-3 - 2 = 0$

$\implies x-1 = 0 \:Or \: x-5= 0$

$\implies x = 1 \:Or \: x = 5$

Therefore.,

$\green { 1 \: and \: 5 \: are \: zeroes \: of }\\\green { \: given \: polynomial . }$

•••♪