Question:- Different between the corresponding roots of x² + ax + b = 0 and x² + bx + a=0 is same and a is not equal to b, then Options: (1) a+b+ 4 = 0. (2) a+b-4 = 0. (3) a-b-4 = 0. (4) a-b+4= 0.
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Verified answer
Answer:
Let x
1
& x
2
be the roots of the equation x
2
+ax+b=0
Therefore, x
1
+x
2
=−a and x
1
x
2
=b
and y
1
& y
2
be the roots of the equation x
2
+bx+a=0
Therefore, y
1
+y
2
=−b and y
1
y
2
=a
Given that, x
1
−x
2
=y
1
−y
2
⇒(x
1
+x
2
)
2
−4x
1
x
2
=(y
1
+y
2
)
2
−4y
1
y
2
⇒a
2
−4b=b
2
−4a
⇒(a−b)(a+b+4)=0
Therefore, a−b=0 or a+b+4=0