Neha Tyagi and Amit Rastogi Solutions for Chapter: Polynomials, Exercise 2: Exercise

Answer the following and justify.

Can the quadratic polynomial $x^2+kx+k$ have equal zeroes for some odd integer $k>1$?

If the zeroes of a quadratic polynomial $a{x}^2+bx+c$ are both positive, then $a, b$ and $c$ all have the same sign.

If the graph of a polynomial intersects the $x-\mathrm{axis}$ at only one point, it cannot be a quadratic polynomial.

If the graph of a polynomial intersects at exactly two points, it need not be a quadratic polynomial.

If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

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.

If all three zeroes of a cubic polynomial $x^3+a{x}^2-bx+c$ are positive, then atleast one of $a, b$ and $c$ is non-negative.

The only value of $k$ for which the quadratic polynomial $k{x}^2+x+k$ has equal zeroes is $\frac{1}{2}$.