Consider the equation

(a) The equation is in the form ax^2 + bx + c

Use those values for b^2 - 4ac.

(-16)^2 - 4*4*25
= 256 - 400
= -144

The determinant is negative, so there will be two imaginary solutions.

(b) The quadratic equation is x = (-b +/- sqrt(determinant))/(2a)

Using the values of a, b, and c from the equation, we get

x = (16 +/- sqrt(-144))/(2*4)
x = (16 +/- 12i)/8
x = 2 +/- 3i/2

Would this be an appropriate answer for b?

x= 4+3i/2, 4-3i/2

How did you get 4 +/- 3i/2?

I figured 4*4 = 16. This is not right is it?

You divide by 8 at the end. 16/8 = 2

(a) To compute the discriminant, we can consider the equation in the form of ax^2 + bx + c = 0, where a = 4, b = -16, and c = 25.

The discriminant, denoted as Δ, is given by the formula: Δ = b^2 - 4ac.

Substituting the values, we have:
Δ = (-16)^2 - 4 * 4 * 25
= 256 - 400
= -144

Since the discriminant, Δ, is negative (-144), there are two different imaginary-number solutions to the equation.

(b) Now, let's use the quadratic formula to find the exact solutions of the equation:

The quadratic formula is given by: x = (-b ± √Δ) / (2a)

Substituting the values, we have:
x = (-(-16) ± √(-144)) / (2 * 4)
= (16 ± √144i) / 8

To simplify further, we can divide the numerator and denominator by 8:
= (2 ± √18i)

Therefore, the exact solutions of the equation 4x^2 – 16x + 25 = 0 are:
x = 2 + √18i
x = 2 - √18i