The relationship between a and b if x = 2 is a root of equation ax^2 - bx + 2 is
Answers
Answered by
2
ax
2
+x+b=0 and x
2
+bx+a=0
have common root and second equation has equal root, then
in second equation
b
2
−4a=0
b=±2
a
So, root of 1
st
equation
=−
2
b
=±
a
1
st
equation
ax
2
+x+b
ax
2
+x+b=0 when x=−
2
b
a
4
b
2
−
2
b
+b=0
b(
4
ab
−
2
1
+1)=0
If, b
=0 so, then a=0
So, 2a
2
+b=0
4
ab
+
4
1
=0
ab=−2
2a
3/2
=−2
a
3/2
=−1 a
=−1 so, 2a
2
+b=0
Answered by
3
Answer:
ax
2
+x+b=0 and x
2
+bx+a=0
have common root and second equation has equal root, then
in second equation
b
2
−4a=0
b=±2
a
So, root of 1
st
equation
=−
2
b
=±
a
1
st
equation
ax
2
+x+b
ax
2
+x+b=0 when x=−
2
b
a
4
b
2
−
2
b
+b=0
b(
4
ab
−
2
1
+1)=0
If, b
=0 so, then a=0
So, 2a
2
+b=0
4
ab
+
4
1
=0
ab=−2
2a
3/2
=−2
a
3/2
=−1 a
=−1 so, 2a
2
+b=0
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