Question

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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Class 10 - Math - Quadratic Equation
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Answer 1

Answer

To prove : 2b = a+c

Step-by-step explanation: Here we have given equal roots so for it , we have , b^2 - 4ac = 0 ------1

compairing given equation with a^2 + bx +c =0 , we get  a = ( b-c) , b= ( c-a) , c = (a-b)

so, putting the values of a,b,c in (1) we get

( c-a )^2 - 4(b-c) ( a -b) =0

solving above  we get  :

a^2 + 4b^2  +c^2 +2ac - 4ab - 4bc = 0

( a +c - 2b)^ 2 = 0

a  + c - 2b = 0

therefore,  2b = a+c         proved.