If the roots of the equation (b – c)x^2 + (c – a)x + (a – b) = 0 are equal, then prove that 2b = a + c.
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solution:Given
the roots of the eqn are equal so,D=0
we know,,
D=b^2--4ac
=(c-a)^2-4(b-c)(a-b)
=c^2+a^2-2ac-4ab+4b^2+4ac-4bc
=a^2-b^2+c^2-4ab-4bc-2ac
=(a-2b+c)^2
=>(a-2b+c)^2=0
rooting on the sides
a-2b+c=0
so,a+c=2b
hence proved
solution:Given
the roots of the eqn are equal so,D=0
we know,,
D=b^2--4ac
=(c-a)^2-4(b-c)(a-b)
=c^2+a^2-2ac-4ab+4b^2+4ac-4bc
=a^2-b^2+c^2-4ab-4bc-2ac
=(a-2b+c)^2
=>(a-2b+c)^2=0
rooting on the sides
a-2b+c=0
so,a+c=2b
hence proved
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