Question

a polynomial ax^4+bx^3+cx^2+dx+c has how many zeros

Answer 1

Answer:

This polynomial has a zero of multiplicity 2 at x=−2 and a zero of multiplicity 2 at x=2. Hence it may be written as

y=a(x+2)

2

(x−2)

2

We now use the y intercept at (0,−2) to write the equation

−2=a(0+2)

2

(0−2)

2

Solve the above for a to obtain

a=−

8

1

We now write the polynomial as follows

y=(−

8

1

)(x+2)

2

(x−2)

2

Expand

y=(−

8

1

)(x

4

−8x

2

+16)

We now identify the coefficients by comparing the polynomial

y=(−

8

1

)x

4

+x

2

−2 by the polynomial y=ax

4

+bx

3

+cx

2

+dx+e we get,

a=−

8

1

, b=0, c=1, d=0, e=−2