Respuesta :
Given:
The given function is [tex]f(x)=4x^2+2x+6[/tex]
We need to determine the value of the discriminant f and also to determine the distinct real number zeros of f.
Discriminant:
The discriminant can be determined using the formula,
[tex]\Delta = b^2-4ac[/tex]
Now, we shall determine the discriminant of the function [tex]f(x)=4x^2+2x+6[/tex]
Substituting the values in the formula, we have;
[tex]\Delta=(2)^2-4(4)(6)[/tex]
[tex]\Delta=4-96[/tex]
[tex]\Delta=-92[/tex]
Thus, the value of the discriminant of f is -92.
Distinct roots:
The distinct zeros of the function f can be determined by
(1) If [tex]\Delta>0[/tex], then the function has 2 real roots.
(2) If [tex]\Delta=0[/tex], then the function has 2 real roots ( or one repeated root).
(3) If [tex]\Delta <0[/tex], then the function has 2 imaginary roots (or no real roots).
Since, the discriminant is [tex]\Delta=-92 \ < \ 0[/tex] , then the function has no real roots or 2 imaginary roots.
Thus, the function has 2 imaginary roots.
