Question

What are the zeros of the polynomial function?


f(x)=x2−12x+20


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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

Answer:

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

Step-by-step 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