If a(b-c)/b(c-a)=b(c-a)/c(b-a)=r such that a, b, c are non-zero distinct real number and r > 0. Find the value of (2r + 1)2
Answers
Answer:
The given equation is 2x
2
+bx+
b
1
=0, comparing it with Ax
2
+Bx+C=0. We get
A=2,B=b and C=
b
1
⇒ B
2
−4AC=(b)
2
−4(2)×
b
1
⇒ B
2
−4AC=b
2
−
b
8
Now,
Discriminant>0 [ For real roots ]
b
2
−
b
8
>0 [ For real roots ]
b
b
3
−(2)
3
>0
b
(b−2)(b
2
+2b+4)
>0
b
2
+2b+4 always positive
b
b−2
>0
b−2>0,b>0 and b−2<0,b<0
b>2 and b<0
b∈(−∞,0)∪(2,∞)
Now, check the options
(A) b+
b
1
>
2
5
b>2 satisfied but b<0 not satisfied
(B) b+
b
1
<
2
5
b>2 not satisfied.
(C) b
2
−3b>−2
b
2
−3b+2>0
b
2
−2b−b+2>0
(b−2)(b−1)>0
b∈(−∞,1)∪(2,∞) satisfied both
Step-by-step explanation: