**Question:**

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.

(iii) Every quadratic equation has atleast two roots.

(iv) Every quadratic equation has atmost 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.

**Solution:**

(i) False, since a quadratic equation has two and only two roots.

(ii) False, for example x2 + 4 = O has no real root.

(iii) False, since a quadratic equation has two and only two roots.

(vi) True, because every quadratic polynomial has atmost two roots.

(v) True, since in this case discriminant is always positive, so it has always real roots, e., ac < 0 and so, b2 – 4ac > 0.

(vi) True, since in this case discriminant is always negative, so it has no real roots e., if b = 0, then b2 – 4ac ⇒ – 4ac < 0and ac>0.

polynomial root calculator, Factoring Polynomials. Factoring a polynomial is the opposite process of multiplying polynomials.