Question

Find all the zeros for each function P(x)=x^4-4x^3-x^2+20x-20

Answer 1

Answer:

The zeros of the given polynomial function are

2,2,$\pm\sqrt{5}$

Step-by-step explanation:

Given polynomial is $P(x)=x^4-4x^3-x^2+20x-20$

To find the zeros equate the given polynomial to zero

ie., P(x)=0

$P(x)=x^4-4x^3-x^2+20x-20=0$

By using synthetic division we can solve the polynomial:

2_|   1     -4     -1      20      -20

       0      2     -4     -10       20

   _____________________

       1     -2      -5      10      |_0

Therefore x-2=0

x=2 is a zero of P(x)

Now we can write the cubic equation as below:

$x^3-2x^2-5x+10=0$

Again using synthetic division

2_|   1     -2     -5     10      

       0      2      0    -10    

    ______________

       1      0      -5     |_0

Therefore x-2=0

x=2 is also a zero of P(x).

Now we have $x^2+0x-5=0$

$x^2-5=0$

$x^2=5$

$x^=\pm\sqrt{5}$ is a zero of P(x)

Therefore the zeros are 2,2,$\pm\sqrt{5}$