Find the Value of q in 3x^2 + qx + 3
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Answer:
Given equations:-
2x+3y=9(p+q)x+(2p−q)y=3(p+q+1)
Here, a2a1=p+q2,b2b1=2p−q3,c2c1=3(p+q+1)9
For a pair of linear equations to have infinitely many solutions:
a2a1=b2b1=c2c1
So, we need, p+q2=2p−q3=3(p+q+1)9
or,p+q2=2p−q3=>2(2p−q)=3(p+q)=>4p−2q=3p+3q=>p=5q....(i)Also,2p−q3=3(p+q+1)9=>9(p+q+1)=9(2p−q)=>p+q+1=2p−q=>2p−p=q+q+1=>p=2q+1Substituting(i),wehave,5q=2q+1=>q=31Also,p=5q=5(31)=35
∴p=35andq=31
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