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?

Discriminant = 84

The polynomial has two real distinct roots

Step-by-step explanation:

Given:

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

Solution:

For a polynomial , discriminant is given by

If , then the polynomial has two real and distinct roots.

If then the polynomial has two real and equal roots.

If D<0 then roots are not real.

Here, in

a = 3, b = 12 and c = 5

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

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116