Question

Find the roots of the quadratic equation a(b-c)x² +b(c-a)x+c(a-b)=0
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Answer 1

Answer ⤵️

If the roots of the equation a(b−c)x2+b(c−a)x+c(a−b)=0 are equal, then the price that b(a+c)=2ac is equal to?

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Discriminant Δ=b2(c−a)2–4ac(b−c)(a−b)

Now a(b−c)+c(a−b)=ab−bc=b(a−c)

∴Δ=(a(b−c)+c(a−b))2–4ac(b−c)(a−b)

=(a(b−c)−c(a−b))2

=(b(a+c)−2ac)2

If the two roots are equal Δ=0⟹

b(a+c)−2ac=0

But I do not know the price aspect