Question

Which two values of x are roots of the polynomial below?

5x2 - 5x+ 1
I A. >=
-8 - 28
6
LUB
5-
45
20
5+5
10
D.
* = 5-15
10
E. X=
5 + 45
20
F.
-8 + 28
XE
6

Answer 1

The two values of x that are roots of the polynomial 5x^2 - 5x + 1 are approximately x = 0.7236 and x = 0.2764. These values were found by applying the quadratic formula and simplifying the results.

Step-by-step explanation:

To determine which two values of x are roots of the polynomial 5x2 - 5x + 1, one must solve the quadratic equation that is obtained by setting the polynomial equal to zero. The general form of a quadratic equation is ax2 + bx + c = 0. Here, a=5, b=-5, and c=1. The quadratic formula for finding the roots of the equation is x = (-b ± √(b2 - 4ac))/(2a).

Plugging the coefficients into the formula gives roots:

x = (5 ± √(((-5)2) - 4(5)(1)))/(2(5)),

x = (5 ± √(25 - 20))/(10),

x = (5 ± √(5))/(10).

Since √(5) is approximately 2.236, we get two possible roots after evaluating for both signs:

x = (5 + 2.236)/10,

x = 0.7236 (approx),

and

x = (5 - 2.236)/10,

x = 0.2764 (approx).

These are the estimated values for the roots of the polynomial 5x2 - 5x + 1.