JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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Analyzing +4 | -1

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}\right]

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)} \text { is }

View answer and explanation

Correct option: D

Option D (3) is correct because the expression simplifies to 3 using the identity

a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)

when

a+b+c=0

, then

a^3 + b^3 + c^3 = 3abc

More Questions from QUADRATIC EQUATIONS

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{x^2} + 4ax + 2 > 0

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