5 questions. Proving (1 Viewer)

[bos1234]

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[jyu]

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For Q1, for all rational values of p, q, NOT for all real values of p, q.

For Q4, 4r > or = s^3, NOT 4r >s^3

 

[bos1234]

i copied the qn exactly for qn 1..
yeah qn 4 ur right..

how do i do them?!?!?!?!?

 

[pyrodude1031]

Question one

those letters can be real .. dont have to be rational.

sum =(p+q)/p = 1+q/p
product = q/p

thereofore , sum = 1+product

for two roots to be rational, their product and sum must also be rational .. (test this with couple of fractions)

since product is already q/p, i.e. rational. See, p q dont have to be rational, SAY, p is pi , and q is e^1, q/p is still rational.. since we cant express it as a fraction.

since sum is just ONE larger than teh product.. then ROOTS ARE RATIONAL.

 

[bos1234]

ah kk got it now.. but y do they say to show that a and c are rational also when a and c are p and q..??

 

[bos1234]

and some1 please answer other qns.. so far i only got qn 1...

 

[jyu]

Question one

those letters can be real .. dont have to be rational.

sum =(p+q)/p = 1+q/p
product = q/p

thereofore , sum = 1+product

for two roots to be rational, their product and sum must also be rational .. (test this with couple of fractions)

since product is already q/p, i.e. rational. See, p q dont have to be rational, SAY, p is pi , and q is e^1, q/p is still rational.. since we cant express it as a fraction.

since sum is just ONE larger than teh product.. then ROOTS ARE RATIONAL.

e/pi is irrational.

Another example q =sqrt3, p = 1, q/p = sqrt3 is irrational.