A quadratic equation is written in the form of ax²+bx+c. The two values of x that are the roots of the polynomial are E and F.
What is a quadratic equation?
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The roots of the quadratic equation are found as shown below,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
If the given equation x²-11x+17 is compared with the general quadratic equation ax²+bx+c, then the value of a, b, and c is 1, -11, and 17, respectively.
The roots of the given polynomial x²-11x+17=0 can be found as shown below. Therefore, The roots of the polynomial are,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\x = \dfrac{-(-11) \pm \sqrt{(-11)^2 - 4(1)(17)}}{2(1)}\\\\x = \dfrac{11 \pm \sqrt{121 - 68}}{2}\\\\x = \dfrac{11 \pm \sqrt{53}}{2}[/tex]
x= (11 + √53)/2 , (11 - √53)/2
Hence, the two values of x that are the roots of the polynomial are E and F.
Learn more about Quadratic Equations:
https://brainly.com/question/2263981
#SPJ5
