Polynomials: CBSE Class 10 Mathematics practice questions

C. $3 - x + 4x^2$

A quadratic polynomial has degree 2, i.e. it has the form $ax^2+bx+c$ with $a\neq 0$. $3-x+4x^2$ has highest power 2, so it qualifies (the order of the terms does not matter). $x^3+4x^2$ is cubic, $2x-7$ is linear, and $x^2+\frac1x$ is not even a polynomial because $\frac1x=x^{-1}$ has a negative power.

A. $-2$

Sum of zeroes $=-\dfrac{-1}{1}=1$, so the other zero is $1-3=-2$. Check with the product: $3\times(-2)=-6=\dfrac{c}{a}$. Slips: $2$ ignores the sign of the product, $-3$ just negates the given zero, and $1$ stops at the sum without subtracting $3$. Direct check: $p(-2)=4+2-6=0$.

C. $-\dfrac{2}{3}$

Sum $=-\dfrac{2}{k}$ and product $=\dfrac{3k}{k}=3$. Setting them equal: $-\dfrac2k=3$, so $k=-\dfrac23$. Slips: $\frac23$ drops the minus sign of the sum; $-\frac32$ comes from inverting wrongly ($k=\frac{3}{-2}$ instead of $k=\frac{-2}{3}$); and $\frac32$ makes both slips at once.