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Nature of Roots

. If the root...

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. If the roots of the equation (b-c) x2 + (c-a) x + (a-b) = 0 are equal, then prove that 2b = a+c.

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Q. If the roots the equation

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

are equal, prove that b + c = 2a.

Q. (a) If the roots of the equation,

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

be equal, then prove thar a,b,c are in arithmetical progression.
(b) If

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

has equal roots, prove that a,b,c are in harmonical progression.

Q. If the roots of the quadratic equation (a-b)x²+(b-c)x+(c-a)=0 are equal prove that 2a=b+c.

Q. If roots is the equation (a–b)x²+(b–c)x+(c–a)=0 are areare equal then prove that 2a=b+c.

Q. If roots of quadratic equation

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

are real and equal then prove that

2 b = a + c

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