(i) Every quadratic equation has exactly one root. (ii) Every quadratic equation has at least one real root.

Monjur Alahi

Write whether the following statements are true or false. Justify your answers.

(i) Every quadratic equation has exactly one root.

(ii) Every quadratic equation has at least one real root.

(iii) Every quadratic equation has at least two roots.

(iv) Every quadratic equations has at most two roots.

(v) If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

(vi) 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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Salim Ahmed Kawsar

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(i) False, for example : x2 = 1 is a quadratic equation with two roots.

(ii) False, for example x2 + 1 = 0 has no real root.

(iii) False, for example : x2+1 = 0 is a quadratic equation which has no real roots.

(iv) True, because every quadratic polynomial has almost two zeroes.

(v) True, because if in ax2+bx+c = 0, a and c have opposite signs, then ac<0

and so b2–4ac > 0.

(vi) True, because if in ax2+bx+c = 0, a and c have same sign and b = 0, then

b2–4ac = –4ac < 0.

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