R. D. Sharma Solutions for Chapter: Polynomials, Exercise 3: EXERCISE 2.3

Find all zeros of the polynomial $2x^4+7x^3-19x^2-14x+30$, if two of its zeros are $\sqrt{2}$ and $-\sqrt{2}$.

If $a$and $b$ are the other two zeroes, then $a+2b=-c$ and $b>a$, find $c.$

Find all the zeros of the polynomial $2x^3+x^2-6x-3$, if two of its zeros are $-\sqrt{3}$ and $\sqrt{3}$.

If $m$ is the other zero of the polynomial and $m=-\frac{1}{2}n$, find $n.$

Find all the zeroes of the polynomial $x^3+3x^2-2x-6$if two of its zeroes are $-\sqrt{2}$ and $\sqrt{2}$ and if $-m$ is the other zero of the polynomial, find $m.$

Find all zeros of the polynomial $2x^4-9x^3+5x^2+3x-1$, if two of its zeros are $2+\sqrt{3}$ and $2-\sqrt{3}$.

If $a$ and $b$ are the other zeroes and $2ab=-c, b>a$. Find $c$.

What must be added to the polynomial $f\left(x\right)=x^4+2x^3-2x^2+x-1$, so that the resulting polynomial is exactly divisible by $x^2+2x-3$?

What must be subtracted from the polynomial $f\left(x\right)=x^4+2x^3-13x^2-12x+21$ so that the resulting polynomial is exactly divisible by $x^2-4x+3$?

If $k$ should be subtracted from the polynomial. What is the value of $k+3$?

Given that $\sqrt{2}$ is a zero of the cubic polynomial $6x^3+\sqrt{2}{x}^2-10x-4\sqrt{2}$, find its other two zeroes.

If $a, b$ are the other two zeroes and $3ab=-m$, find $m.$

Given that $x-\sqrt{5}$ is a factor of the cubic polynomial $x^3-3\sqrt{5}{x}^2+13x-3\sqrt{5}$, find all the zeroes of the polynomial.

If $a \text{and} b$ are the other roots of the polynomial and $ab=m$. Find $m$.