Question

see the attachment. and ans the question maths​

Answer 1

Answer:

2/9×(2p-q)(2q-p)

Step-by-step explanation:

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Alpha and Beta are roots of x^2-px+r=0

We can say

alpha +beta =p.........(1) (alpha)(beta)=r...............(2)

alpha/2 and 2beta are root of x^2-qx+r=0

So,

alpha/2 +2beta=q ..............(3). (alpha/2)(2beta)=r..............(4)

2(1)-(2)

2alpha-alpha/2 +2beta-2beta=2p-q

so

3alpha /2=2p-q

alpha=2(2p-q)/3

Substituting in eq1

We get beta=p-4p/3+2q/3=(2q-p)/3

So we know

(alpha)(beta) =r=2/9×(2p-q)(2q-p)

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