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15. If f(x)=x...

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15. If f(x)=x2 + ax+b be an integral funtion of the integral variable x then 1 a is an integer and b is arational fraction 2 a and b are integer 3 b is an integer and a is a rational fraction 4 a and b are rational fraction

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Q. In each of the following state if the statement is true (T) or false (F):
(i) The quotient of two integers is always an integer.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction
(vi) If

\frac{a}{b}

is a rational number and m any integer, then

\frac{a}{b} = \frac{a \times m}{b \times m}

(vii) Two rational numbers with different numerators cannot be equal.
(viii) 8 can be written as a rational number with any integer as denominator.
(ix) 8 can be written as a rational number with any integer as numerator.
(x)

\frac{2}{3} is equal to \frac{4}{6} .

If a is an integer and b is a rational number, then the number of rational numbers between a and b is

State True or False.

A rational number can always be written in a fraction

\frac{a}{b}

, where a and b are not integers

(b \neq 0)

.

Q. Assertion :If

a

b

are integers and the roots of

x^{2} + a x + b = 0

are rational then they must be integers. Reason: If the coefficient of

x^{2}

in a quadratic equation is unity then its roots must be integers.

a, b, c

be positive integer such that

\frac{a \sqrt{2} + b}{b \sqrt{2} + c}

is a rational number, then which of the following is always an integer?

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