Answer:
There are 2 real solutions for 5x^2 + 7x + 2.
Explanation:
- 5x^2 + 7x + 2 is in the standard form of a quadratic equation.
The general equation of the standard form is given by:
ax^2 + bx + c = 0
or
ax^2 + bx + c = y, where:
- a, b, and c are constants.
We can determine how many solutions there are for the quadratic using the discriminant (D), which comes from the quadratic given by.
It is b^2 - 4ac and it has and i can tell us one of three things about the real solutions to a quadratic:
- When D < 0, there are 0 real solutions.
- When D = 0, there is 1 real solution.
- When D > 1, there are 2 real solutions.
Since 5 = a, 7 = b, and 2 = c, we can substitute these values for the variables in the discriminant formula to determine how many real solutions there are:
D = 7^2 - 4(5)(2)
D = 49 - 40
D = 9
9 > 0
Since the discriminant (9) is greater than 0, there are 2 real solutions for 5x^2 + 7x + 2.