Question

If α , β are the roots of the equation 2x²-5x+7=0 , then equation whose roots are (2α+3β) and (3α+2β) is.​

Answer 1

Step-by-step explanation:

this is correct answer

Answer 2

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Let alpha=p and beta =q.

p and q are the roots of the equation ax^2+bx+c=0. therefore:-

p+q = -b/a……………(1).

p.q= c/a………………..(2).

Sum of the roots = 2p+3q+3p+2q =5(p+q)= -5b/a.

Product of the roots =(2p+3q).(3p+2q)= 6(p^2+q^2)+13p.q.

= 6.{(p+q)^2 -2p.q} +13.p.q.

=6.(p+q)^2 -12.pq+13.pq.

=6(p+q)^2+p.q.

=6.b^2/a^2. +c/a = (6b^2+a.c)/a^2.

Required equation is:-

x^2-(sum of roots).x+ product of roots =0

or. x^2+5(b/a).x+(6b^2+ac)/a^2=0

or. a^2.x^2+5a.b.x +(6b^2+ac)= 0.