Using the discriminant, what values of c will make the quadratic y = -4x2 + 5x + c have no real solutions?

A)
(-∞, -25/16)

B)
(-∞, -25/16]

C)
(-25/16, ∞)

D)
[-25/16, ∞)

Question

Using the discriminant, what values of c will make the quadratic y = -4x2 + 5x + c have no real solutions?
	

A)
	(-∞, -25/16) 	
	

B)
	(-∞, -25/16] 	
	

C)
	(-25/16, ∞) 	
	

D)
	[-25/16, ∞)

zepdrix · Answer

$\large y=-4x^2+5x+c$

Using the Quadratic Formula:

$\large x=\dfrac{-b\pm\color{orangered}{\sqrt{b^2-4ac}}}{2a}$

We only care about this orange part, the discriminant.
Plugging in our values gives us,$$\large \sqrt{b^2-4(a)(c)}\qquad \rightarrow\qquad \sqrt{5^2-4(-4)(c)} \qquad \rightarrow\qquad \sqrt{25+16c}$$

So what they're asking essentially is, `what values of c will cause us to take the square root of a negative number`?