Question

if the roots of the equation a minus b into X square + b minus C Into X + c minus A is equal to zero are equal prove that twice a is equal to b + c​

Answer 1

Answer:

b + c = 2a

Step-by-step explanation:

If the roots of the equation a minus b into X square + b minus C Into X + c minus A is equal to zero are equal prove that twice a is equal to b + c​

(a - b)x² + (b-c)x + (c-a) = 0

Roots are equal if

(b-c)² = 4(a-b)(c-a)

=> b² + c² - 2bc = 4(-a² + ab + ac - bc)

=>  b² + c² + 2bc = -4a² + 4a(b + c)

=> (b + c)² = -4a² + 4a(b + c)

=> (b + c)² - 2a(b+c) =  -4a² + 2a(b + c)

=> (b + c)(b + c - 2a) = 2a(b + c - 2a)

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

=> b + c = 2a

Answer 2

Answer:

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