Statement (1) : If a and b are integers and roots of `x^2 + ax + b = 0` are rational then they must be integers. Statement (2): If the coefficient of `x^2` in a quadratic equation is unity then its roots must be integers
A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.
A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.
Correct Answer – C
Let `(p)/(q), (p,q in Z, , q ne 0 and HCF (p, q) = 1)` be a root of `x^(2) + ax + b = 0`. Then, `(p^(2))/(q^(2))+(ap)/(q) + b = 0`
`rArr” “p^(2) + apq + bq^(2) = 0`
`rArr” “p^(2) = -q (ap + bq)`
`rArr” “q “divides” p^(2)” “[therefore q “divides-q”(ap + bq)]`
`rArr” “q “divides p”” “[therefore HCF (p, q) = 1]`
`rArr” “q = 1” “[therefore HCF (p, q) = 1]`
Thus `x^(2) + ax + b = 0` has integer roots.
So, statement-1 is true.
Statement-2 is false as `x^(2) + x + 1 = 0` does not have integer roots.