Because 13 is a prime number, we cannot use the AC method to simplify.
We can instead use the quadratic formula.
[tex]\frac{-b +/- \sqrt{b^2 - 4ac} }{2a}[/tex]
11 +/- √121 - 52 / 2
11 +/- √69 / 2
11 +/- 8.3 / 2
(11 + 8.3)/2 = 9.65
(11 - 8.3)/2 = 1.35
Answer:
[tex]x=\frac{11+\sqrt{69}}{2}[/tex] and [tex]x=\frac{11-\sqrt{69}}{2}[/tex]
Step-by-step explanation:
[tex]x^2-11x+13[/tex]
13 is a prime number . we cannot factor it because we cannot find two factors whose product is 13 and sum is -11. Apply quadatic formula to find the x values
Given polynomial is in the form of ax^2+bx+c
a= 1, b= -11 and c=13
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
Plug in the values in the formula
[tex]x=\frac{11+-\sqrt{(-11)^2-4(1)(13)}}{2(1)}[/tex]
[tex]x=\frac{11+-\sqrt{69}}{2(1)}[/tex]
[tex]x=\frac{11+\sqrt{69}}{2}[/tex] and [tex]x=\frac{11-\sqrt{69}}{2}[/tex]
