Question

how many real solutions does the equation have?
$w^2 + 69 = 0$
no real solution
one real solution
two real solutions
submit

Explanation:

Step1: Analyze the quadratic equation form

The equation is \( w^2 + 69 = 0 \), which can be rewritten as \( w^2=- 69 \).

Step2: Determine real solutions

For a real number \( w \), the square of \( w \) (i.e., \( w^2 \)) is always non - negative (because if \( w\) is real, \(w^2\geq0\)). But here we have \( w^2=-69 \), and \(- 69<0\). So there are no real numbers \( w \) that satisfy this equation.

Answer:

no real solution