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