Polynomials (Class 10 Maths)

Q1. If $x-2$ is a factor of $p(x)=x^2-kx+8$, then the value of $k$ is

Q2. For $p(x)=x^3-ax^2+bx-6$, if $x-1$ and $x-2$ are factors and the remainder when $p(x)$ is divided by $x-3$ is $6$, then $a+b=$

Q3. The cubic polynomial $p(x)=x^3-3x^2-kx+12$ has zeroes $\alpha,\beta,\gamma$. If $\alpha+\beta=\gamma$, then the value of $k$ is

Q4. A monic cubic polynomial has zeroes $1,-2,m$. If the remainder when it is divided by $x-3$ is $8$, then the coefficient of $x^2$ is

Q5. A quadratic polynomial gives remainders $2,5,10$ when divided by $x-1$, $x-2$, and $x-3$ respectively. Which polynomial fits these values?

Q6. Which of the following is a factor of $2x^2-7x+3$?

Q7. If $\alpha$ and $\beta$ are the zeros of $x^2-5x+m$, and $\alpha^2+\beta^2=13$, then the value of $m$ is:

Q8. If $p(x)=x^3-ax^2+bx-6$ leaves remainder $2$ when divided by $x-1$ and remainder $0$ when divided by $x-2$, then $a+b$ equals:

Q9. Let $p(x)=x^3-3x^2-kx+3k$. If one zero of $p(x)$ is $3$ and the sum of squares of all its zeros is $29$, then $k$ is:

Q10. If the zeros of $p(x)=x^2-(m+1)x+m$ differ by $3$, then the set of all possible values of $m$ is:

Q11. If $p(x)=3x^2-7x+k$ and $p(2)=5$, what is $k$?

Q12. For the polynomial $p(x)=x^2-(m+1)x+m$, the zeros differ by $1$. Which of the following is the set of all possible values of $m$?

Q13. A quadratic polynomial $p(x)$ satisfies $p(1)=4$ and $p(-2)=-8$. What is $p(3)$?

Q14. A polynomial $p(x)$ leaves remainder $4$ when divided by $x-1$ and remainder $12$ when divided by $x-3$. If $p(x)$ is divided by $x^2-4x+3$, what is the remainder?

Q15. The zeros of $p(x)=x^2+ax+b$ are $\alpha$ and $\beta$, and they satisfy $\alpha-\beta=1$ and $\alpha^2+\beta^2=13$. What is the value of $b$?