Question

Obtain other zeroes of the polynomial
f(x) = 2x4 + 3x3 - 5x2 - 9x - 3
if two of its zeroes are √3 and - √3.​

Answer 1

$\text{Given zeros are}$

$\text{ \sqrt{3} and -\sqrt{3} }$

$\text{Sum of the zeros=0}$

$\text{Product of the zeros= (\sqrt{3})(-\sqrt{3})=-3 }$

$\text{Corresponding quadratic factor is}$

$x^2-3$

$\text{Now,}$

$2x^4+3x^3-5x^2-9x-3=(x^2-3)(2x^2+px+1)$

$\text{Equating coefficients of x on both sides, we get}$

$-9=-3p$

$\implies\bf\,p=3$

$\text{Other factor is}$

$2x^2+3x+1$

$=2x^2+2x+x+1$

$=2x(x+1)+1(x+1)$

$=(2x+1)(x+1)$

$2x^2+3x+1=0\implies\;x=-1,\;\frac{-1}{2}$

$\therefore\textbf{The other two zeros are -1 and \bf\frac{-1}{2} }$

Answer 2

Answer:

Step-by-step explanation:  hope  helpful for you