Question

If the roots of the equation(a+b)x^2 + (b+c)x + (c+a) = 0 are equal,prove 2a = b+a

Answer 1

Step-by-step explanation:

we know that

if the quadratic equation ax²+bx+c=0 whose roots are equal then it's determinant is equal to zero.

(a-b)x²+(b-c)x+(c-a)a=0

determinant =0

(b-c)²-4(a-b)(c-a) =0

b²+c²-2bc-4ac+4a²+4bc-4ab =0

b²+c²+4a²+4bc-4ac-4ab=0

b²+c²+(-2a)²+2bc+2c(-2a)+ 2(-2a)b=0

(b+c-2a)²=0

b+c-2a=0

therefore b+c=2a

or 2a=b+a

hence proved

Answer 2

plz refer to this attachment