a When we solve quadratics using the Quadratic Formula, the number of solutions is determined by the discriminant. When the discriminant is greater than zero, our equation, x^2-4kx+36=0 will have two solutions. Let's start by substituting a= 1, b= -4k, and c=36 into the appropriate discriminant equation, d>0, to solve for k.
When taking the square root of an inequality, sometimes you need to check values around both roots to determine the direction of the inequality for each solution. In this case, if k>3 or k<-3, our equation will have two solutions.
b When the discriminant is equal to zero, our equation, x^2-4kx+36=0 will have one solution. Let's start by substituting a= 1, b= -4k, and c=36 into the appropriate discriminant equation, d=0, to solve for k.
In this case, if k=3 or k=-3, our equation will have two solutions.
c When the discriminant is less than zero, our equation, x^2-4kx+36=0 will have no solutions. Let's start by substituting a= 1, b= -4k, and c=36 into the appropriate discriminant equation, d<0, to solve for k.
When taking the square root of an inequality, sometimes you need to check values around both roots to determine the direction of the inequality for each solution. In this case, if -3
