Question

Which of the following is/are always false ? (a) A quadratic equation with rational coefficients has zero or two irrational roots. (b) A quadratic equ

Quadratics
ANSWERED
asked 2020-12-12
Which of the following is/are always false ?
(a) A quadratic equation with rational coefficients has zero or two irrational roots.
(b) A quadratic equation with real coefficients has zero or two non - real roots
(c) A quadratic equation with irrational coefficients has zero or two rational roots.
(d) A quadratic equation with integer coefficients has zero or two irrational roots.

Answers (1)

2020-12-13
It is known that a quadratic equation that have rational coefficient can have zero, rational or irrational roots.
But the quadratic equations that have irrational coefficient has only zero or irrational coefficient.
Thus, the statement "(c) A quadratic equation with irrational coefficients has zero or two rational roots ." is always false.
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