Find all values of h which the quadratic equation has no real solutions

Question

4x²+3x+h = 0

Answer 1

We all know the quadratic formula x=(-b +- sqrt(b^2-4ac))/2a

To answer this we just need to focus on the discriminant...the portion of the quadratic formula under the square root: b^2-4ac

For a quadratic equation to have no real answers the discriminant must be less than zero. For our problem here a=4 b=3 and c=h so we want

3^2-4*4*h<0

9-16h<0

9<16h

9/16<h

So all values of h for which 4x²+3x+h = 0 has no real solutions is any h greater than 9/16

TEST...h=2>9/16. 3^2-4*4*2=-21<0

Answer 2

The discriminant of Ax² + Bx + C is B² - 4AC

The equation Ax² + Bx + C = 0 has no real solutions when the discriminant is negative.

So, 4x² + 3x + h = 0 has no real solutions when 3² - 4(4)(h) < 0

-16h < -9

h > 9/16.