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

The value of Discriminant of the function is -92

It has ZERO distinct real number zeros.

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=(-2+√(-92) )/(8)`

or

`x=(-2-√(-92) )/(8)`

the term
`√(-92)` is imaginary

hence the zeros are not real number