if a+b+c=0 in ax^2+bx+c=0,then the roots are
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Step-by-step explanation:
a+b+c=0
b=−a−c
⇒b=−(a+c)
given by ax
2
+bx+c
D=b
2
−4ac
=(−(a+c))
2
−4ac ,(putting the value of b)
=(a+c)
2
−4ac=a
2
+c
2
+2ac−4ac
=a
2
+c
2
−2ac
=(a−c)
2
thus, the root
2a
−b±
D
=
2a
−b±
(a−c)
2
thus, we can conclude that if discriminant is a perfect square then root are rational
(p+q)x
2
−2px+(p−q)=0
D=(−2p)
2
−4(p+q)(p−q)
=4p
2
−4(p
2
−q
2
) (as(a+b)(a−b)=(a
2
−b
2
))
=4p
2
−4p
2
+4q
2
=4q
2
=(2q) 2
=
2a
−b+a−c
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