f(x) = 4x^2+2x+6 What is the value of the discriminant of f? How many distinct real number zeros does f have?

Answer:The value of Discriminant of the function is -92It has ZERO distinct real number zeros. Step-by-step explanation:Given:[tex]f(x)=4x^{2} +2x+6[/tex]Which is a Quadratic Equation in the general form of[tex]ax^{2}+bx+c=0[/tex]where a,b and c are constants.So on comparing the given equation with general form we get,[tex]a=4\\b=2\\c=6[/tex]Formula for discriminant we have[tex]Discriminant=b^{2}-4ac\\ =2^{2}-4(4)(6)\\ =4-96\\=-92[/tex]now for zeros  we have[tex]x=\frac{-b+\sqrt{b^{2-4ac} } }{2a} \\or\\x=\frac{-b-\sqrt{b^{2-4ac} } }{2a} \\[/tex]on substituting these values we get[tex]x=\frac{-2+\sqrt{-92} }{8}[/tex]or[tex]x=\frac{-2-\sqrt{-92} }{8}[/tex]the term [tex]\sqrt{-92}[/tex] is imaginaryhence the zeros are not real number