Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
A quadratic equation with integral coefficient has integral roots. Justify your answer.
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If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
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If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
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Every quadratic equations has at most two roots.
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Every quadratic equation has at least two roots.
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Every quadratic equation has at least one real root.
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