Determine the $x$-intercept(s) of the quadratic function
$f ( x ) = x ^ { 2 } - 10 x + 26$.
A) $( 0,0 ) , ( 4,0 )$
B) $( 5,0 ) , ( 10,0 )$
C) $( 7,0 ) , ( 2,0 )$
D) $( 0,0 ) , ( 2,0 )$
E) no $x$-intercept(s)

Question

Determine the $x$-intercept(s) of the quadratic function 
$f ( x ) = x ^ { 2 } - 10 x + 26$.
A) $( 0,0 ) , ( 4,0 )$
B) $( 5,0 ) , ( 10,0 )$
C) $( 7,0 ) , ( 2,0 )$
D) $( 0,0 ) , ( 2,0 )$
E) no $x$-intercept(s)

Quizplus · Accepted Answer

To find the $x$-intercepts of the quadratic function $f(x) = x^2 - 10x + 26$, we set $f(x) = 0$ and solve for $x$. This gives us the equation $x^2 - 10x + 26 = 0$. The discriminant of this quadratic equation is $b^2 - 4ac = (-10)^2 - 4(1)(26) = 100 - 104 = -4$. Since the discriminant is negative, the equation has no real roots, meaning the function has no $x$-intercepts.

Determine The xxx -Intercept(s) of the Quadratic Function f(x)=x2−10x+26f ( x ) = x ^ { 2 } - 10 x + 26f(x)=x2−10x+26

Determine The $x$ -Intercept(s) of the Quadratic Function $f ( x ) = x ^ { 2 } - 10 x + 26$