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If roots of the equation  are rational numbers, then which of the following cannot be true?

a)

All  are even

b)

All  are odd

c)

 is even while  are odd

d)

None of the above



Question ID - 104919 | SaraNextGen Top Answer

If roots of the equation  are rational numbers, then which of the following cannot be true?

a)

All  are even

b)

All  are odd

c)

 is even while  are odd

d)

None of the above

1 Answer
127 votes
Answer Key / Explanation : (b) -

(b)

For rational roots  must be a perfect square of a rational number and as  are natural numbers  must be a perfect square of an integer.

 are both odd integers or both even integers but  is an odd integer. So,  and  must be even integers.   is odd  must be odd. Now, let

,  odd integer)

 odd integer)

 is an even integer)

So, contradiction  is not a perfect square. So, all  cannot be odd integers.

127 votes


127