Question

Find the number of real number solutions for the equation. x2 + 5x + 7 = 0

0

2

1

cannot be determined

Answer 1

0 real solutions in this equation.

Answer 2

Steps:

• Discriminant Formula: D = b² - 4ac (With a = x² coefficient, b = x coefficient, and c = constant)

So to find the number of solutions this quadratic equation has without actually solving the equation, we are going to be using the discriminant formula. Plug in the numbers and solve:

`D=5^2-4*1*7\\D=25-28\\D=-3`

Now, here are the rules with discriminants:

• D > 0; there are 2 real solutions in the equation
• D = 0; there is 1 real solution in the equation
• D < 0; there are no real solutions in the equation

Answer:

Since -3 is less than 0, this means that there are 0 real solutions in this equation.