Question

how many real solutions does the equation have?
$r^3 + 27 = 0$
no real solution
one real solution
two real solutions
submit

Explanation:

Step1: Analyze the equation \( r^2 + 27 = 0 \)

We can rewrite it as \( r^2 = - 27 \).

Step2: Recall the property of square of real numbers

For any real number \( r \), the square \( r^2 \) is always non - negative (i.e., \( r^2\geq0 \)). But here we have \( r^2=-27 \), and \(-27<0\). So there is no real number \( r \) that satisfies this equation.

Answer:

no real solution