Find the possible values of k for which the graph of y= 4x^2-3x+k, does not intersect the x-axis

Question

agent0smith · Answer

For a graph to have no intercepts, the discriminant must be a negative number. For a quadratic ax^2 + bx + c, the discriminant is $$\Large b^2 - 4 ac$$

So you want to set that less than zero, and solve for k
 $$\Large 3^2 - 4*4*k < 0$$

anonymous · Answer

k<9/16?

agent0smith · Answer

Your numbers are right, but it looks like you forgot one step.

If you divide or multiply an inequality by a negative number, the sign changes direction.

anonymous · Answer

k<-9/16?

agent0smith · Answer

I'm guessing you got to here, then divided both sides by -16 $$\Large -16k < -9$$
$$\Large k > 9/16$$

anonymous · Answer

thats the answer? thank you

anonymous · Answer

how about this one.The roots of 2kx^2+6 = x^2+8x are equal what is the value of k?

agent0smith · Answer

Well you almost had it, just remember that when dividing by a negative, the direction of the inequality sign changes.