In the following, determine whether the given values of x are zeroes ofthe given polynomial or not:
x ²+(√2)x – 4 ; x =√2, x = -2√2

Let p(x) = x ² + (√2)x – 4
Put x =√2

If x = √2 is a zero of the polynomial p(x), then it must satisfy p(√2) = 0.

So, on putting x = √2 in the above equation, we get:

p(√2) = (√2) ² + √2(√2) - 4

= (2) + (2) - 4

= 4 – 4

= 0.

Therefore the given value of x is a zero of the given polynomial.
If x = -2√2 is a zero of the polynomial p(x), then it must satisfy p(-2√2) = 0.

So, on putting x = -2√2 in the above equation, we get:

p(-2√2) = (-2√2) ² + √2(-2√2) - 4

= (8) - (4) - 4

= 8 – 8

= 0.

Therefore the given value of x is not a zero of the given polynomial.