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

Answer:

Discriminant = 84

The polynomial has two real distinct roots

Step-by-step 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.