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.