Question

Consider the function f(x) = 3x2 + 7x + 2.

What is the value of the discriminant?
-17
25
31
73
How many x-intercepts does this function have?
0
1
2
3
What are the number of zeros for this function?
zero real number solutions
one real number solution
two real number solutions

Answer 1

b, c, c

Explanation:

edge 2021

Answer 2

Hello from MrBillDoesMath!

Answer:

Discriminant = 25

2 x intercepts

two real number solutions ( -(1/3) and -2)

Discussion:

For a quadratic polynomial ax^2 + bx + c = o the discriminant is given by

b^2-4ac. In our case a = 3, b = 7, and c =2, so the discriminant =

7^2 - 4(3)(2) = 49 - 24 = 25

X-intercept is where 3x^2 + 7x + 2 = 0. As the above discriminant is positive, their are 2 solution to the quadratic equation

There are two real number solutions for this function:

x = ( -b +\= sqrt(b^2 - 4ac) /2a)

= (- 7 +\- sqrt (7^2 - 4(3)(2) ) /2*3

The two solutions are

(-7 + sqrt(25))/6 = ( -7 + 5 ) /6 = -2/6 = - (1/3)

and

(-7 - sqrt(25))/6 = ( -7 - 5 ) /6 = -12/6 = - 2

Thank you,

MrB