Are all real numbers, rational numbers ?

No,all real nos. are not rational nos.

Let us see the definition of rational number.

A rational number is a number of the form p/q where p, q are integers with q not equal to 0. The set of rational numbers is denoted by Q.

Examples: all integers ……..-3,-2,-1,0,1,2,3………. Because any integer say 2 can be written as 2/1 which satisfies the definition of rational number. All fractions for instance, 3/4, -5/13, etc., are also rational numbers.

They can be converted into either terminating decimals like 3.25, 5.497, etc., or recurring decimals like 5.3535353535….., 6.471471471……

Those decimals which are neither terminating nor recurring are called irrational numbers. The set of irrational numbers is denoted by Q’.

Examples of irrational numbers are 2.65478354690153854……….., 23.5473569364520914…………

Other two good examples of irrational numbers are e and π.

The set of real numbers, denoted by R, is the union of these two disjoint sets ,Q the set of rational numbers and Q’ the set of irrational numbers.

Conclusion: The set of rational numbers forms a proper subset of real numbers.

i.e., all rational numbers are real numbers but not vice versa.

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

you could deduce the conclusion directly using the facts pertaining to the specific situation.

hope this .