Question

The number of integral values of x if the following statement is valid? 0≤x2≤100.
a)19
b)20
c)22
d)21
Please help today is my exam it is really urgent please explain the answer properly.​

Answer 1

The number of integral values of x satisfying 0≤x²≤100 is 21

Therefore, option (d) is correct.

Step-by-step explanation:

Given

$0\le x^2\le 100$

The value of x should be such that its square is less than 100

Square of any number is always greater than or equal to zero

Thus,

$x^2\le 100$

$\implies x^2-100\le 0$

$\implies x^2-10^2\le 0$

$\implies (x-10)(x+10)\le 0$

$\implies x\in[-10, 10]$

Thus, the integral values of x are

$-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10$

Total number of values = 21

Hope this answer is helpful.

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