Find all other zeroes of the polynomial 2x3 + 3x2 - 11x - 6, if one of its zero is -3.
Answers
Answer:
divide this cubic polynomial with x+3=0 and then you get a quadratic polynomial with after middle term break will give two factors , thereby the other two zeroes
Step-by-step explanation:
Step-by-step explanation:
\textbf{Given:}Given:
p(x)=2x^3+3x^2-11x-6\;\text{and one of its zero is -3}p(x)=2x
3
+3x
2
−11x−6and one of its zero is -3
\textbf{To find:}To find:
\text{All other zeros of p(x)}All other zeros of p(x)
\textbf{Solution:}Solution:
\text{Since -3 is a zero of $p(x)$,we use sythetic division to find}Since -3 is a zero of p(x),we use sythetic division to find
\text{all other zeros of p(x)}all other zeros of p(x)
\textbf{By synthetic division,}By synthetic division,
\begin{gathered}\begin{array}{r|cccc}-3&2&3&-11&-6\\&&-6&9&6\\\cline{2-5}&2&-3&2&|\,0\end{array}\end{gathered}
−3
\cline2−5
2
2
3
−6
−3
−11
9
2
−6
6
∣0
\textbf{Quotient}=2\,x^2-3\,x-2Quotient=2x
2
−3x−2
2\,x^2-3\,x-2=02x
2
−3x−2=0
2x^2-4\,x+x-2=02x
2
−4x+x−2=0
2x(x-2)+1(x-2)=02x(x−2)+1(x−2)=0
(2x+1)(x-2)=0(2x+1)(x−2)=0
\implies\bf\,x=\dfrac{-1}{2},\,2⟹x=
2
−1
,2
\textbf{Answer:}Answer:
\textbf{All other zeros of $p(x)$ are $\bf\dfrac{-1}{2}$ and $2$}All other zeros of p(x) are
2
−1
and 2
Find more:
Obtain other zeroes of the polynomial
f(x) = 2x4 + 3x3 - 5x2 - 9x - 3
if two of its zeroes are √3 and - √
Find all the zeros of of the polynomial 2x^4+7x^3-19x^2-14x+30 if two of its zeroes are root 2 and -root 2