How do you find the discriminant and how many and what type of solutions does #x^2 + 5x + 7 = 0# have?
See a solution process below:
The quadratic formula states:
The discriminate is the portion of the quadratic equation within the radical:
If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions
To find the discriminant for this problem substitute:
Because the number is negative you will get two complex solutions.
A standard polynomial form is:
From your equation:
∴ 25 - 4 x 1 x 7
A negative discriminant means there is no real root.
If you wanted to go further, it would have complex x roots. But yeah: