Question

Find the number of real number solutions for the equation. x^2+5x+7=0

A.0
B. 1
C. cannot be determined
​

Answer 1

Given a quadratic equation
`ax^2+bx+c=0`, we define the discriminant as

`\Delta = b^2-4ac`

The number of real solutions of the equation depend on the sign of
`\Delta`:

• If
  `\Delta>0` the equation has two solutions
• If
  `\Delta=0` the equation has one double solution
• If
  `\Delta<0` the equation has no real solutions

In this case, we have

`\Delta = 25-28=-3<0`

And so this equation has no real solutions.