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Vimala Desai
Asked: 2022-11-04T05:27:51+05:30 In:

If a, b `in` R, then the equation `x^(2) – abx – a^(2) = 0` has
A. one positive and one negative root
B. both positive roots
C. both negative roots
D. non-real roots

If a, b `in` R, then the equation `x^(2) – abx – a^(2) = 0` has
A. one positive and one negative root
B. both positive roots
C. both negative roots
D. non-real roots
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1 Answer

  1. Correct Answer – A
    Let `alpha , beta` be the roots of the givn equation. Then, `alpha + beta = ab and alpha beta = – a^(2)`
    Also, Disc `= a^(2)b^(2) + 4a^(2) gt 0`.
    Thus, `alpha, beta in R` such that `alpha beta lt 0`.
    Therefore, one of `alpha and beta` is positive and other is negative.

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