Decide whether the statement is true or false. If it is false, tell why.
-If $k$ is a positive number, then the equation $-x^{2}=-100 k$ has no real solutions.
A) True
B) False; the equation is equivalent to $x^{2}=100 k$, where $x^{2}$ and $100 k$ are positive, so it will have two real solutions
C) False; the equation is equivalent to $x^{2}=100 k$, where $x^{2}$ and $100 k$ are positive, so the equation will have one real number solution

Question

Quizplus · Accepted Answer

The equation $-x^{2}=-100 k$ simplifies to $x^{2}=100 k$. Since $k$ is positive, $100 k$ is also positive, meaning $x^{2}$ is positive. This results in two real solutions for $x$, as a positive square root has both a positive and negative solution.

Decide Whether the Statement Is True or False kkk Is a Positive Number, Then the Equation

Decide Whether the Statement Is True or False $k$ Is a Positive Number, Then the Equation