Let \alpha be a root of the equation (a-c) x^2+(b-a) x+(c-b)=0 where a, b, c are distinct real numbers such that the matrix \left[\begin{array}{ccc}\alpha^2 & \alpha & 1 \ 1 & 1 & 1 \ a & b & c ]\end{array} is singular. Then the value of \frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)} is [24-Jan-2023 Shift 1]

JEE Mains 24-Jan-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 72 of 90

Marks: +1, -0

Let α be a root of the equation
(a−c)x2+(b−a)x+(c−b)=0 where a,b,c are distinct real numbers such that the matrix
[

]
is singular. Then the value of ‌

(a−c)2

(b−a)(c−b)

+‌

(b−a)2

(a−c)(c−b)

+‌

(c−b)2

(a−c)(b−a)

[24-Jan-2023 Shift 1]

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