Are the following statements ‘True’ or ‘False’? Justify your answers.
- (i)If the zeroes of a quadratic polynomial ax2 + 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 be 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 x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative. (vii) The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is
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(i) If the zeroes of a quadratic polynomial ax2 + 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 be 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 x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative. (vii) The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is