Determine the $x$-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 6 x + 10$.
A) $( - 8,0 ) , ( 1,0 )$
B) $( - 3,0 ) , ( 7,0 )$
C) $( - 1,0 ) , ( - 6,0 )$
D) $( - 8,0 ) , ( - 6,0 )$
E) no $x$-intercept(s)

Question

Quizplus · Accepted Answer

The discriminant of the quadratic equation $x^2 + 6x + 10 = 0$ is $b^2 - 4ac = 6^2 - 4(1)(10) = 36 - 40 = -4$, which is less than 0. This means the equation has no real roots, and thus the graph of the function does not intersect the $x$-axis, indicating no $x$-intercepts.

Determine The xxx -Intercept(s) of the Quadratic Function f(x)=x2+6x+10f ( x ) = x ^ { 2 } + 6 x + 10f(x)=x2+6x+10

Determine The $x$ -Intercept(s) of the Quadratic Function $f ( x ) = x ^ { 2 } + 6 x + 10$