| Statement-1: If \[{{x}^{2}}+px+q\] is an integer for every odd integral value of x, then p & q are necessarily odd integers. |
| Statement-2: Sum of two odd integers is an even integer |
A) Statement -1 is true, statement -2 is true and statement-2 is correct explanation for statement -1.
B) Statement -1 is true, statement -2 is true and Statement-2 is NOT 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: D
Solution :
Let \[f(x)={{x}^{2}}+px+q\] Let\[p=q=\frac{k}{2};k\in l\] \[\therefore \]\[f(x)={{x}^{2}}+\frac{k}{2}(x+1)=\]integer for every odd value of x so it is not necessary that p & q are odd integers.
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