Question

If the roots of the equation (b-c)x*2+(c-a)x+(a-b)=0are equal then.Prove that 2b=a+c​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given:

$(b - c) x{}^{2} + (c - a)x + (a - b) = 0$

To Prove:

$2b = a + c$

How to Solve?

We can solve by using Discriminant.

What is discriminate?

The discriminant is the part of the quadratic equation in which contains (coefficient of x)² - 4(coefficient of x²)(constant). The discriminant tells us whether there are two solutions, one solution, or no solutions.

When the quadratic equation has equal roots then the discriminant is equal to zero.

Solution:

Comparing the (b - c)x² +(c - a)x + (a - b) = 0 equation from basic equation Ax² + Bx + C = 0, I get....

A = (b - c), B = (c - a) , C = (a - b)

Since Roots are equal So discriminate is

B² - 4AC = 0

See in the attachment