Obtain all other zeros of the polynomial 2x4 + 3x3
-5x2
-9x-3 ,if two of its zeros
are √3 and - √3
Answers
Step-by-step explanation:
2X4+3X3-5X2-9X-3
X=√3 =>(X-√3) -----(1)
X= -√3 => (X+√3) --------(2)
form (1) and (2)
( X-√3)(X+√3)=0
X(X+√3) -√3(X+√3)=0
X²+√3X - √3X -3 =0
X²-3=0
g(x)=X²-3
p(x)=2X4+3X3-5X2-9X-3
since, the following p(x) and g(x) equation divided them and they for into zeroes :
2x²+3x+1
______________
X²-3√2x4+3x3-5x2-9x-3
2x4. -6x2
- +
-----------------------------
3x3+x2-9x-3
3x3. -9x
- +
----------------------------
x² -3
x² -3
- +
--------------------------
0000000
-------------------
r(x)=2x²+3x+1
q(x)=x²-3
since, the r(x) equation spilliting the method
=2x²+3x+1
= 2x²+2x+1x+1
= 2x(x+1) + 1(x+1)
= (2x+1)(x+1)
=> x= -1/2
=> x= -1