Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        If (cosx+sin(ax) is a periodic function and a is a root of equation x2+px+q=0 where p,q belong to integers , then show that pq cannot be an odd integer.`
8 years ago

16 Points
```										Dear harshit agarwal,
Given (cosx+sin(ax)) is a periodic function
This implies that 'a' should be rational.
'a' is root of x2+px+q=0, where p, q are integers.
As 'a' is rational number, let us consider a = m/n, where m,n are coprimes.
(m/n)2 + p(m/n) + q = 0.
m2 + pmn + qn2 = 0
m2 = -n(pm+qn)
hence m should be divisible by n, but m,n are coprimes, hence n=1, hence the equation will be
m2 +pm + q = 0, m is an integer.
q = -m(m+p)
It is clear that q is divisible by m.
If m is even then q is even and p can be even or odd.
If m is odd and p is odd then q is even
If m is odd and p is even then q is odd.
These are possible cases which doesn't include the case in which both q, p are odd.
if q is odd, then m should be odd and m+p should be odd
i.e., if q is odd, then m should be odd and p should be even.
Hence, pq cannot be odd integer.

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation. All the best harshit agarwal

Regards,
nagesh

```
8 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details
Get extra Rs. 1,272 off
USE CODE: Neerajwin
Get extra Rs. 187 off
USE CODE: Neerajwin