if the equation ( 1 + m ^2 ) x ^2 + 2mcx + c ^2 - a ^2 =0 has equal roots . Find the values of c in terms of a and m
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Answered by
1
Answer:
Given equation is (1+m
2
)x
2
+2mcx+c
2
−a
2
=0
We need to prove c
2
=a
2
(1+m
2
)
The roots are real and equal Δ=0.
Therefore, b
2
−4ac=0
⇒(2mc)
2
−4(1+m
2
)(c
2
−a
2
)=0
⇒4m
2
c
2
−4(c
2
−a
2
+m
2
c
2
−m
2
a
2
)=0
⇒m
2
c
2
−(c
2
−a
2
+m
2
c
2
−m
2
a
2
)=0
⇒m
2
c
2
−c
2
+a
2
−m
2
c
2
+m
2
a
2
=0
⇒c
2
=a
2
+a
2
m
2
⇒c
2
=a
2
(1+m
2
)
Answered by
0
Answer:
I donot get your questions
Step-by-step explanation:
please arrange it
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