Question

28) If the roots of the quadratic equation (b - c)^2 +(c - a)x + (a - b) = 0 are equal
then show that 2b=a+ c
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Answer 1

Given quadratic equation is

(b - c)² +(c - a)x + (a - b) = 0

We are told that the quadratic equation

(b - c)² +(c - a)x + (a - b) = 0 has two equal roots.

So, (c-a)²-4(a-b).(b-c) = 0

=> c²-2ca+a² - 4(ab-ca-b²+bc) = 0

=> c²-2ca+a² - 4ab+4ca+4b²-4bc = 0

=>c²+2ca+a² - 4ab +4b² -4bc = 0

=> (c+a)² +4b² = 4ab +4bc

=> (c+a)² +4b²= 4b (a+c)

=> 4b² = 4b (c+a) - (c+a)²

=> 4b²= (c+a)(4b-c-a)