if a, b, c are integers, P.T. roots of equation (b – c) x² + (c – a) x + (a – b) = 0 are rational​

Question

if a, b, c are integers, P.T. roots of equation (b – c) x² + (c – a) x + (a – b) = 0 are rational​

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Sophia 3 weeks 2021-11-07T09:16:17+00:00 1 Answer 0 views 0

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    2021-11-07T09:17:17+00:00

    Answer:

    Yes it is rational

    Step-by-step explanation:

    We have, (b+c−a)x2+(c+a−b)x+(a+b−c)=0

    D=(c+a−b)2−4(b+c−a)(a+b−c)=(a+b+c−2b)2−4(a+b+c−2a)(a+b+c−2c)=(−2b)2−4(−2a)(−2c)=4(b2−4ac)=4((−a−c)2−4ac)=4(a−c)2=(2(a−c))2

    which is a perfect square.

    Hence roots are rational.

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