Question

What are the zeros of the polynomial function?

f(x)=x2−12x+20


Enter your answers in the boxes.


The zeros of f(x) are

and

Answer 1

Hello from MrBillDoesMath!

Answer:

x = 2 and 10

Discussion:

Approach 1:

20 = (-10)*(-2) and (-10) + (-2) = -12 the coefficients of the polynomial. Hence

x^2 -12x + 20 = ( x- 2) * ( x-10)

Approach 2:

From the quadratic formula ( a = 1, b = -12, c = 20)

x = ( -(-12) +\- sqrt( ((-12)^2 - 4*1*20) ) / (2 * 1)

= ( 12 +\- sqrt( 144-80) ) /2

= (12 +\- sqrt(64) ) /2

= (12 +\- 8 ) /2

x = ( 12 + 8) /2 = 20/2 = 10

or

x = ( 12 - 8)/ 2 = 4/2 = 2

Thank you,

MrB

Answer 2

The zeros of the function are 2 and 10. The points are (2,0) and (10,0).

Explanation:

To solve for the zeros, factor the polynomial function.

`f(x) = x^2-12x+20\\f(x) = (x-2)(x-10)\\`

To solve for x, set each factor equal to 0.

x-2 = 0 so x=2

x-10 = 0 so x=10