Question

How many real-number solutions does the quadratic equation 2x^2 + 7x + 9 = 0 have?

Answer 1

We are given the following equations:

$2x^2+7x+9=0$

This is an equation of the form:

$ax^2+bx+c=0$

To determine the number and type of solutions we can use the discriminant of the equation. The discriminant is determined by the following number:

$\Delta=b^2-4ac$

Now, we plug in the values:

$\Delta=(7)^2-4(2)(9)$

Now, we solve the operations:

$\Delta=-23$

The number and type of solutions are given by the following conditions:

$\begin{gathered} \Delta>0,\text{ two real solutions} \\ \Delta=0,\text{ one real solutions} \\ \Delta=\text{ two complex solutions} \end{gathered}$

Since we get that:

$\Delta=-23<0$

Therefore, the equation has two complex solutions and therefore, no real number solution.