Are the following statements 'True' or 'False'? Justify your answer.
(i) If the zeroes of a quadratic polynomial `ax^(2) +bx +c` are both positive, then a,b and c all have the same sign.
(ii) If the graph of a polynomial intersects the X-axis at only one point, it cannot be a quadratic polynomial.
(iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not ve a quadratic polynomial.
(iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
(v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
(vi) If all three zeroes of a cubic polynomial `x^(3) +ax^(2) - bx +c` are positive, then atleast one of a,b and c is non-negative.
(vii) The only value of k for which the quadratic polynomial `kx^(2) +x +k` has equal zeroes is `(1)/(2)`.

Answer

No, `x^4 -1` is a polynomial intersecting the x-axis at exactly two points.