Find All The Zeroes Of The Polynomial $ 3x^{3}+10x^{2}-9x-4$, If One Of Its Zeroes Is 1.
Given: The Polynomial $ 3x^{3}+10x^{2}-9x-4$
To do: Find all the zeros of the polynomial if one of its zero is 1
Solution:
One of the zeros of the given cubic polynomial is 1 (given)
Using Horner method dividing the polynomial
1 | 3 + 10 -9 -4
0 3 13 4
-----------------
3 13 4 0
The quadratic factor of the cubic polynomial is $3x^{2} + 13x + 4$
= $3x^{2} + 12x + x + 4 = (3x + 1)(x + 4)$
So the other two zeros of the cubic polynomial are $\frac{-1}{3}$ and -4
Related Articles
- Find all zeroes of the polynomial $3x^3\ +\ 10x^2\ -\ 9x\ –\ 4$, if one of its zeroes is 1.
- Find all zeroes of the polynomial $( 2x^{4}-9x^{3}+5x^{2}+3x-1)$ if two of its zeroes are $(2+\sqrt{3}) and (2-\sqrt{3)}$.
- Obtain all zeroes of the polynomial $f(x)\ =\ x^4\ –\ 3x^3\ –\ x^2\ +\ 9x\ –\ 6$, if the two of its zeroes are $-\sqrt{3}$ and $\sqrt{3}$.
- Find all zeroes of the polynomial $f(x)\ =\ 2x^4\ –\ 2x^3\ –\ 7x^2\ +\ 3x\ +\ 6$, if two of its zeroes are $-\sqrt{\frac{3}{2}}$ and $\sqrt{\frac{3}{2}}$.
- Obtain all other zeroes of $3x^4 + 6x^3 - 2x^2 - 10x - 5$, if two of its zeroes are $\sqrt{\frac{5}{3}}$ and $-\sqrt{\frac{5}{3}}$.
- Obtain all zeroes of the polynomial $f(x)\ =\ 2x^4\ +\ x^3\ –\ 14x^2\ –\ 19x\ –\ 6$, if two of its zeroes are $-2$ and $-1$.
- If a polynomial $x^4+5x^3+4x^2-10x-12$ has two zeroes as $-2$ and $-3$, then find the other zeroes.
- Find all zeros of the polynomial $2x^4\ -\ 9x^3\ +\ 5x^2\ +\ 3x\ -\ 1$, if two of its zeros are $2\ +\ \sqrt{3}$ and $2\ -\ \sqrt{3}$.
- Find the zeroes of polynomial: $q( x)=\sqrt{3}x^2+10x+7\sqrt{3}$.
- If $\sqrt{3}$ and $-\sqrt{3}$ are the zeroes of $( x^{4}+x^{3}-23 x^{2}=3 x+60)$, find the all zeroes of given polynomial.
- Find all the zeroes of the polynomial $x^4\ +\ x^3\ –\ 34x^2\ –\ 4x\ +\ 120$, if the two of its zeros are $2$ and $-2$.
- 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 one of the zeroes of the quadratic polynomial $( k-1)x^{2}+kx+1$ is $-3$, then find the value of $k$.
- If two zeroes of the polynomial $x^4 - 6x^3 - 26x^2 + 138x - 35$ are $2 \pm \sqrt3$, find other zeroes.
- If the sum of zeroes of the quadratic polynomial $3x^2–kx+6$ is $3$, then find the value of $k$.
Kickstart Your Career
Get certified by completing the course
Get Started