Question

f(x) = 3x^2+12x+5f(x)=3x 2 +12x+5f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 12, x, plus, 5 What is the value of the discriminant of fff? How many distinct real number zeros does f(x)f(x)f, left parenthesis, x, right parenthesis have?

Answer 1

The discriminant of F is 84

F has 2 distinct real number zeros

Explanation:

Answer 2

Discriminant = 84

The polynomial has two real distinct roots

Explanation:

Given:
`f(x)=3x^2+12x+5`

To find: discriminant of the given function and number of distinct real zeros

Solution:

For a polynomial
`f(x)=ax^2+bx+c` , discriminant is given by
`D=b^2-4ac`

If
`D>0`, then the polynomial has two real and distinct roots.

If
`D=0` then the polynomial has two real and equal roots.

If D<0 then roots are not real.

Here, in
`f(x)=3x^2+12x+5`

a = 3, b = 12 and c = 5

`D=(12)^2-4(3)(5)=144-60=84`

As D > 0, the polynomial has two real distinct roots.