Question

. If two zeroes of a polynomial x4

– x

3

– 3x2

+3x are 3 and –3, then find the other two zeroes.​

Answer 1

Answer:

0000000000000000000000000000000000

Answer 2

The other two zeroes for the given polynomial are x=1 and 0

Step-by-step explanation:

• Given polynomial is $x^4-x^3-3x^3+3x$
• Also given that $\sqrt{3}$ and $\sqrt{-3}$ are the two zeroes for the given polynomial.

To find the other two zeroes :

• To find zeroes first equate the given polynomial to zero
• That is $x^4-x^3-3x^2+3x+0=0$

By Synthetic Division we can find zeros

1_|  1     -1     -3     3    0

      0     1      0    -3    0

  __________________

      1      0     -3    0     0

• Therefore x-1 is a factor of the given polynomial
• x-1=0

Therefore x=1 is a zero

Now we have the cubic equation $x^3+0x^2-3x+0=0$

• $x^3-3x=0$
• $x(x^2-3)=$
• $x=0$ or $x^2-3=0$
• $x^2=3$

• $x=\pm \sqrt{3}$

Therefore $x=\sqrt{3},\sqrt{-3}$

Therefore $x=1,0,\sqrt{3},\sqrt{-3}$ are the zeroes

Hence the other two zeroes for the given polynomial are x=1 and 0