Embibe Experts Solutions for Chapter: Polynomials, Exercise 1: Nagaland Board-2020

If $\alpha$ and $\beta$ are the zeroes of polynomial $2x^2-4x+5$, then find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$.

If the polynomial $x^4+2x^3+8x^2+12x+18$ is divided by $x^2+5$ and the remainder is in the form of $px+q$, find the value of $p$ and $q$.

A quadratic polynomial whose zeros are $-5$ and $1$ is 

If the zeroes of the polynomial $a{x}^2+bx+c$ are in ratio $3:4$, then prove that $12b^2=49ac$.

If the sum of squares of zeros of the quadratic polynomial $3x^2+5x+k$ is $\frac{-2}{3}$, then the value of $k$ is

If one root of the quadratic equation $a{x}^2+bx+c=0$ is three times the other, then $b^2:ac$ is equal to

Find the quadratic equation whose one root is $1+\sqrt{2}$ and the sum of its roots is $2$. 

If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $6x^2-\left(k+1\right)x-7x$ such that one zero is $\frac{11}{6}$ more than the other, find the value of $k$.