Question

verify whether 2 and 0 are zeroes of the polynomial x square -2x

Answer 1

$f(x) = {x}^{2} - 2x \\ f(2) = {2}^{2} - 2 \times 2 = 4 - 4 = 0 \\ f(2) = 0 \\ f(0) = {0}^{2} - 2 \times 0 = 0 \\ so \: 2 \: and \: 0\: both \: are \: zeroes \: of \: polynomial$
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Answer 2

Given:

Verify whether 2 and 0 are zeroes of polynomial $\sf{x^2 -2x}$

To Verify :

Whether 2 and 0 are zeroes of polynomial $\sf{x^2 -2x}$

Solution:

Given polynomial is  $\sf{x^2 -2x}$

Let p(x) be the given polynomial

$\sf{x^2 -2x}$

To verify that 2 and 0 are zeroes of polynomial

p(x) we have to put x=2 and x=0 in p(x) and hence it must satisfies the polynomial.

$\: \: \: \: \: \: \: \fbox{ p(x)=0 for x=2 and 0} \orange\bigstar$

Now put x=2 in p(x)

$\sf{p(2)=2^2-2(2)} \\ \: \: \sf{=4 - 4} \\ \: \: \: \: \: \: \: \: \: \: \: \boxed {\frak{p(2) =0}} \pink\bigstar$

Now put x=0 in p(x)

$\sf{p(0)=0^2-2(0)} \\ \: \: \sf{=0-0} \\ \: \: \: \: \: \: \: \: \: \: \: \boxed {\frak{p(0) =0}} \blue\bigstar$

• Hence, 0 and 2 both satisfy that they are zero of the polynomial.
• The given polynomial p(x) is a quadratic polynomial. Hence, a quadratic polynomial has two zeroes.

Thank you!

@itzshivani