Are the following statements 'True' or 'False'? Justify your answers. (i) If the zeroes of a quadratic polyno…

Mathematics Polynomials

Are the following statements 'True' or 'False'? Justify your answers.

(i)If the zeroes of a quadratic polynomial $a x^{2} + b x + c$ 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 $x^{3} + a x^{2} - b x + c$ 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 $k x^{2} + x + k$ has equal zeros is $\frac{1}{2}$ .

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