Question

find the zeros of polynomial f x is equals to x square - 2 and verify the relation between its zeros and coefficients​

Answer 1

Solution:

Let @ and ß be the zeros of given polynomial

Given polynomial:

$f(x) = x {}^{2} - 2$

$f(x) = x {}^{2} - 2 \\ \: \: \: \: \: \: \: \: \: \: = x {}^{2} - \sqrt{2 {}^{2} } \\ \: \: \: \: \: \: \: \: \: \: = (x - \sqrt{2})(x + \sqrt{2} )$

Now,

f(x)=0

=>(x+√2)(x-√2)=0

=>x=-√2 or x=√2

=>@=-√2 and ß=√2

Sum of zeros:

@ + ß

= -√2 +√2

=0

Product of zeros:

@ß

=(-√2)(√2)

=-2

Hence,verified.

The sum and product of zeros the following rules,

sum of zeros: -x coefficient/x^2 coefficient

product of zeros: constant term/x^2 coefficient