InterviewSolution
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InterviewSolution
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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 atleast one real root. (ii) Every quadratic equation has atleast two roots. (iv) Every quadratic equations atmost two roots. (v) If he coefficient of `x^(2)` and the constnat term of a quadratic equation have opposite sigh, then the quadratic equation has real roots. (vi) If the coefficient of `x^(2)` 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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Answer» (i) False since a quadratic equation has two and onloy two roots. (ii) False, for example `x^(2)+4=0` has no real root. (iii) False, Since a quadratic equations has to only two roots (iv) True, because every quadratic polynomial has atmost two roots. (v) True, since in this cae discriminant is always positive, so it has always real roots i.e. `aclt0` and so `b^(2)-4acgt0` (vi) True, Since in this case discriminant is always negative so it has no real roots i.e. , if `b=0` then `b^(2)-4acimplies-4aclt0` and `acgt0`. |
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