Question

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 1

Discriminant is -92

0 distinct real number zeros.

Answer 2

Answer:

The value of Discriminant of the function is -92

It has ZERO distinct real number zeros.

Step-by-step explanation:

Given:

$f(x)=4x^{2} +2x+6$

Which is a Quadratic Equation in the general form of

$ax^{2}+bx+c=0$

where a,b and c are constants.So on comparing the given equation with general form we get,

$a=4\\b=2\\c=6$

Formula for discriminant we have

$Discriminant=b^{2}-4ac\\ =2^{2}-4(4)(6)\\ =4-96\\=-92$

now for zeros  we have

$x=\frac{-b+\sqrt{b^{2-4ac} } }{2a} \\or\\x=\frac{-b-\sqrt{b^{2-4ac} } }{2a}$

on substituting these values we get

$x=\frac{-2+\sqrt{-92} }{8}$

or

$x=\frac{-2-\sqrt{-92} }{8}$

the term $\sqrt{-92}$ is imaginary

hence the zeros are not real number